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[Assistant] From here you open the door and you wait several seconds. You pick up the leash and say, okay, then walk the dog outside.


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[Assistant] Okay. Heel. Okay. Good. There you go. Here. Good boy. That was nice. Come here. That was good. That was good.


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[Assistant] If your dog moves prior to the okay command, go back a step in the process. Repeat and condition the behavior.


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[Assistant] Your dog should wait for your okay command before going anywhere.


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[Assistant] Okay, gaww, there you go, nice. Good boy. Good boy. Good boy.


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[Assistant] If you have a sliding door, or a dog that likes to dash out of a car, the technique is all the same.


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[Assistant] Fireheart waited until the only sound he could hear was the pounding of blood in his ears. Then he padded to the edge of the thunder path. It stretched ahead of him, wide and foul smelling, but silent. Fireheart darted out. The ground beneath his paws felt cold and smooth. He didn't stop until he reached the grass on the other side.


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[Assistant] The air here was tainted by the acrid smell of the thunder path and its monsters, so Fireheart headed toward the hedge. Still, there was no trace of the Windclan cats. His heart sank.


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[Assistant] Suddenly a monster tore past, making Fireheart leap into the air with terror.


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[Assistant] He scrambled underneath the hedge and crouched, trembling, frantically wondering what to do next. Then, he smelled it.


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[Assistant] There was a pause, then the sound of paws pounding across the thunder path to join him. Have you found it? puffed his friend. Not sure. I got a whiff, but I can't pinpoint it. Fireheart pushed his way through the hedge, Graystripe right behind him. He lifted his nose toward the open field ahead of them. Have you any idea what's over there? No, replied Graystripe.


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[Assistant] I shouldn't think any clan cat have ever been this far before. Except WindClan, muttered Fireheart darkly.


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[Assistant] Away from the confusing fumes of the thunder path, the trail was suddenly clear. WindClan had definitely come this way.


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[Assistant] He saw a thunder path ahead of them arching high into the air on massive stone legs, illuminated by the eyes of the monsters that moved along it.


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[Assistant] Another thunder path ran below, veering off into the darkness. Greystripe nodded toward a tall thistle. And smell this. Fireheart inhaled the scent. It was a fresh wind clan marker. They must have settled somewhere near here. Greystripe murmured in disbelief. A pang of excitement twisted Fireheart's stomach. Both cats looked silently at each other for a moment. Ben, without a word.


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[Assistant] They moved on toward the stinking thunder paths. Greystripe spoke at last. Why would Windclan come to a place like this? I guess not even Brokenstar would wanna follow them here, Fireheart answered grimly. He stopped, a thought was nagging at him. Greystripe paused beside him. What is it? If Windclan is hiding so near the thunder paths, Fireheart meowed slowly.


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[Assistant] They're more likely to trust us if we arrive in daylight than if we creep up on them in darkness.


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[Assistant] Does that mean we can rest? Asked Graystripe, sitting down heavily. Just until it's light, meowed Fireheart. We'll find somewhere to hide and see if we can get some sleep. Are you hungry? Graystripe shook his head. Me neither, Fireheart agreed.


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[Assistant] I don't know if it's those herbs or because the stench from the thunder path is making me feel sick. Where shall we sleep? Greystripe looked around.


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[Assistant] Fireheart had already noticed a dark shadow in the ground up ahead. What's that? A burrow? Greystripe sounded puzzled. It's too big for a rabbit. Surely there can't be a badger set here. Let's take a look, Fireheart suggested. The hole was larger than a badger set, smooth and lined with stone.


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[Assistant] Fireheart sniffed it, then put his front paws on its rim, and peered cautiously inside.


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[Assistant] After a few fox lengths, the slope leveled out. Fireheart halted and sniffed the damp air. He could smell nothing but the fumes of the thunder path. A roaring noise rumbled overhead.


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[Assistant] Fireheart's paws trembled as the stone floor vibrated. Was the thunder path above them?


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[Assistant] He closed his stinging eyes and thought of the gentle forest breezes and the rustling of the leaves.


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[Assistant] Exhaustion fought briefly with a pang of longing to be at home in his den, before he gave in to the blackness that swam into his mind.


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[Assistant] When Fireheart opened his eyes again, gray light was glowing at the end of the tunnel. Dawn must be near.


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[Assistant] Fireheart's bones ached from the cold hard ground. He nudged Graystripe, who grunted. Mourning already? Almost, Fireheart answered, getting to his paws. Graystripe stretched and stood up too.


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[Assistant] I think we should head that way. Fireheart meowed, craning his neck away from the light. I think this tunnel leads right under a thunder path. It might take us nearer to the- His voice trailed off.


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[Assistant] He had no words to describe the tangle of thunder paths they had seen last night. Beside him, Greystripe nodded.


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[Assistant] And together they began to pad wordlessly into the darkness. Before long Fireheart spotted light ahead of them.


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[Assistant] They quickened their pace until they were racing up a short steep slope that led them into a world filled with grey dawn light.


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[Assistant] They had come up near the edge of a patch of barren, dirty grass. Thunder paths enclosed it on two sides and another arched overhead. A fire burned in the middle of the grass. A few two legs lay around it.


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[Assistant] One of them stretched and rolled over, and another grunted angrily in its sleep.


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[Assistant] And his mind flooded with the memory of his dream.


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[Assistant] The noise of the thunder path, the sight of the flames and the cats, and spotted leaves voice murmuring, fire will save the clan. A surge of emotion made Fireheart's legs feel weak.


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[Assistant] Did this mean that ThunderClan's fate was bound up with the fate of WindClan? Fireheart? Fireheart? Greystripe's voice jolted Fireheart back to reality. He breathed deeply to calm himself. We must find Tallstar and speak with him, he meowed. Then you think it is WindClan? Asked Greystripe. You smelled their marker. Who else could it be? Fireheart replied.


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[Assistant] Greystripe looked at him, his eyes shining with triumph. We found them! Fireheart nodded.


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[Assistant] He didn't point out that finding Wen Clan was only half their mission. They still had to convince them that it was safe to return home. Greystripe braced himself, ready to leap forward. Let's go! Hang on, Fireheart warned. We don't want to startle them. Just then.


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[Assistant] One of the two legs sat up with a jolt and began shouting at the ragged cats around the fire.


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[Assistant] All caution forgotten, Fireheart and Graystripe raced after them.


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[Assistant] Fireheart could feel his fur prickle with fear as he and Graystripe ran straight toward the fire in the two legs.


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[Assistant] Every instinct told him to keep away, but he dared not lose sight of the fleeing Windclam cats.


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[Assistant] One of the two legs staggered to its feet, looming up in front of him.


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[Assistant] Fireheart skidded, sending up a spray of dust. Something exploded beside him, pelting him with hard edged splinters. But nothing pierced his thick coat. He glanced backward, checking for gray stripes.


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[Assistant] They charged into the safety of the shadows beneath the soaring thunder path.


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[Assistant] Ahead, Fireheart watched the Wind Clan cats stop close to one of the Thunderpath's great stone legs. And then, one by one, the cats disappeared into the ground. Where did they go, meowed Graystripe in amazement. Another tunnel, Fireheart suggested. Come on, let's find out. Cautiously.


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[Assistant] The two friends approached the spot where the Windclang cats had vanished. As they neared, they saw a hole in the earth.


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[Assistant] Like their resting place on the previous night, the entrance was round and lined with stone, sloping away into utter blackness.


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[Assistant] Fireheart led the way, all his senses alert for a Windclam patrol.


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[Assistant] The floor beneath his paws felt wet and slimy, and the sound of trickling water echoed around them.


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[Assistant] As the tunnel levelled out, Fireheart pricked his ears and opened his mouth. The damp air smelled rank and bitter, worse than the tunnel they had slept in. Here, the Thunderpath fumes mingled with the fear scent of Windclan cats.


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[Assistant] It was too dark to see anything but after a few paces, Fireheart's whiskers sensed a turning in the tunnel.


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[Assistant] Fireheart flicked his tail, touching gray stripe lightly with its tip.


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[Assistant] He couldn't see his friend in the blackness but Greystripe must have felt the signal because he stopped beside Fireheart and together they peered around the corner. Ahead of them.


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[Assistant] The tunnel was lit by a narrow hole in the ceiling that led to the wasteland above.


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[Assistant] Fireheart could see many cats huddled together in the grey light. Warriors and elders, queens and kits. All pitifully thin.


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[Assistant] A cold breeze blew relentlessly through the hole in the roof, stirring the thin fur on the skinny bodies. Fireheart shuddered.


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[Assistant] A grey wind clan tom spun around, his fur standing on end as he yowled an alarm to the rest of the clan.


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[Assistant] In one smooth movement, the Wind Clan warriors formed a line across the tunnel in front of the queens and elders, their backs arched, hissing fiercely. With a feeling of dread.


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[Assistant] Fireheart saw the glint of unsheathed claws and thorn-sharp fangs.


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[Assistant] These half-starved cats were about to attack.


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[Assistant] Firepaw returned with a chaff inch gripped firmly between his teeth. He dropped it in front of Tigerclaw, who stood waiting in the hollow. You're the first one back, mailed the warrior. Yeah, but I've got loads more prey to fetch, Firepaw muted quickly. I buried it back. I know exactly what you did, Tigerclaw growled. I've been watching you. A swish of bushes announced Graypaw's return.


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[Assistant] He was carrying a small squirrel in his mouth, which he dropped beside Firepaw's chaff inch. Yuck, he spat. Squirrels are too furry. I'll be picking hairs out of my teeth all evening. Tigerclaw paid no attention to Graypaw's grumbling. Raven paused late, he observed. We'll give him a bit longer and then return to camp.


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[Assistant] But what if he's been bitten by an adder? Firepaw protested.


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[Assistant] Then it's his own fault, Tigerclaw replied coldly. There's no room for fools in ThunderClan. They waited in silence.


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[Assistant] Greypaw and Firepaw exchanged glances, worried about Ravenpaw.


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[Assistant] Tiger Claws sat motionless, apparently lost in his own thoughts.


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[Assistant] Firepaw was the first to send Ravenpaw's arrival.


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[Assistant] Hey! Meowed Greypaw, rushing forward to admire Ravenpaw's catch. Did that bite you?


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[Assistant] I was too quick for it, Ravenpaw purred loudly. Then he caught Tigerclaw's eye and fell silent.


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[Assistant] Tigerclaw fixed all three excited apprentices with a cold stare. Come on, he said shortly. Let's collect the rest of your prey and get back to camp.


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[Assistant] Firepaw, Graypaw, and Ravenpaw entered the camp strolling behind Tigerclaw.


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[Assistant] Their impressive day's catch hung from their mouths, although Ravenpaw kept tripping over his dead snake.


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[Assistant] As they emerged from the gorse into the camp, a group of young kids scrambled out of the nursery to watch them pass. Look, Firepaw heard one of them say.


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[Assistant] He recognized the little tabby yellow tail had hissed at the day before. Sitting next to him was a fluffy gray kit, no more than two moons old.


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[Assistant] A tiny black kit and a small tortoise shell stood beside them.


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[Assistant] Graypaw mewed again, as the apprentices dropped their catch for the other cats to share. What should I do with it? Asked Ravenpaw, sniffing the snake's long body as it lay beside the heap. Can you eat at Earth? Asked Graypaw. Trust you to think of your stomach, Firepaw joked, butting Graypaw with his head. Well, I wouldn't want to eat it, murmured Ravenpaw.


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[Assistant] Let's put it on the tree stump then, suggested Graypaw, so that Dustpaw and Sampaw can see it when they get back.


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[Assistant] They each carried a piece of their fresh kill, and the adder backed their den.


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[Assistant] Greypaw carefully placed the adder on the stump, arranging the snake so that it could be seen clearly from all sides. Then, they ate.


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[Assistant] When they had finished, they sat close together to groom one another and talk. I wonder who Bluestar will choose to go to the gathering, Firepaw meowed. It'll be full moon tomorrow. Sampaw and Dustpaw have been twice already, replied Graypaw. Perhaps Bluestar will choose one of us this time, mewed Firepaw. After all, we've been training for almost three moons now.


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[Assistant] Firepaw jumped up immediately and bounded off across the clearing toward Bluestar's den.


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[Assistant] Bluestar was sitting outside, her tail flicking restlessly back and forth.


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[Assistant] When she saw Fire Paul, she stood up and looked steadily down at him.


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[Assistant] Tiger Claw has told me that he saw you talking with a cat from the two leg place today. She meowed quietly. But, Firepaw began. He said that you began by fighting with this cat, but ended up sharing tongues with it. That's true, Firepaw admitted, feeling his fur prickle defensively. But he was an old friend. We grew up together. He paused and swallowed.


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[Assistant] Do you miss your old life, Firepaw, she asked. Think carefully now. No. How can Bluestar think that, Firepaw wondered. His head was spinning. What was Bluestar trying to make him say? Do you wish to leave the clan? Of course not, Firepaw was shocked by her question. Bluestar didn't seem to hear the passion in his answer. She shook her head, looking suddenly old and tired.


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[Assistant] I won't judge you if you leave us, Firepaw. Perhaps I expected too much of you.


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[Assistant] Perhaps my judgment has been clouded by the clan's need for new warriors.


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[Assistant] Panic swept through Firepaw at the thought of leaving the clan forever. But my place is here! This is my home! He protested. I need more than that, Firepaw.


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[Assistant] I need to be able to trust in your loyalty to ThunderClan especially now that it looks like ShadowClan is planning an attack.


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[Assistant] We don't have room for anyone who isn't sure whether their heart lies in the past or the present. Firepaw took a deep breath and chose his next words carefully.


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[Assistant] What life would have been like if I had stayed with the two legs. I felt happy that I had not stayed. I was proud I left. He held Bluestar's gaze without flinching.


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[Assistant] Meeting Smudge made me certain I made the right decision.


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[Assistant] I could never have been satisfied with the soft life of a kitty pet. Bluestar looked closely at him for a moment, her eyes narrow. Then she nodded. Very well, she said. I believe you. Firepaw dipped his head respectfully and let out a silent sigh of relief. I spoke to Yellowfang earlier, meowed Bluestar in a lighter tone. She thinks a lot of you.


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[Assistant] She's a wise old she-cat, you know. And I suspect she wasn't always bad-tempered. Indeed, I think that I could grow to like her.


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[Assistant] Firepaw felt an unexpected glow of pleasure at these words.


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[Assistant] Maybe in caring for Yellowfang, his admiration for her had grown into affection, despite the She-Cat's ill temper. Whatever the reason, he was glad Bluestar liked her too. But there is something about her that I don't trust, Bluestar went on quietly. She will stay with ThunderClan for now, but remain as a prisoner. The Queens will care for her. You must concentrate on your training.


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[Assistant] Firepaw nodded and waited to be dismissed, but Bluestar hadn't finished. Firepaw.


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[Assistant] Although you showed bad judgement today in talking to a house cat, Tigerclaw was impressed by your hunting skills. In fact, he reported that you all did well. I am pleased with your progress. You will come to the gathering. All three of you.


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[Assistant] Firepaw could hardly stand still, his body tingled with excitement. The gathering? What about Sampaw and Dustpaw? He mewed. They will remain behind and guard the camp, replied Bluestar. Now you may go. She flicked her long tail to show he was dismissed and returned to her grooming.


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[Assistant] Greypaw and Ravenpaw looked stunned to see Firepaw bounding happily toward them. They had been waiting nervously for him beside the tree stump. Firepaw sat down and looked at his friends. Well, Greypaw demanded, what did she say?


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[Assistant] Tigerclaw told us you'd been sharing tongues with a kitty pet this morning. Burst out Ravenpaw. Are you in trouble? No.


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[Assistant] Although Bluestar wasn't pleased, Firepaw admitted ruefully. She thought I might want to leave ThunderClan. You don't, do you? Asked Ravenpaw. Of course he doesn't, mute Graypaw. Firepaw gave his Gray friend an affectionate swipe.


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[Assistant] Yeah, you'd hate that. You need me to catch mice for you. All you can catch these days are hairy old squirrels.


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[Assistant] Greypaw dodged out of the way of Firepaw's blow and reared up on his back legs to retaliate.


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[Assistant] You'll never guess what else she said, Firepaw went on. He was too excited to waste time play fighting. Greypaw immediately dropped back onto all four paws. What? He asked. We're going to the gathering.


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[Assistant] Greypaw led out a yowl of delight and bounded up onto the tree stump. One of his back paws knocked the adder flying. It hit Ravenpaw on the head and wrapped itself around his neck.


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[Assistant] Ravenpaw spat with alarm and surprise and then turned on Graypaw. Watch it, he hissed crossly. He shook the adder onto the ground. Scared it might try to bite you, Firepaw teased.


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[Assistant] He leaped onto Firepaw and rolled him easily onto his back.


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[Assistant] Greypaw reached down from the tree stump and gave Ravenpaw's tail a tug.


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[Assistant] As Ravenpaw turned to Thumpgreypaw with a soft Fourpaw,


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[Assistant] Firepaw jumped to his feet and leaped into them both sending Graypaw flying from the stump.


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[Assistant] All three cats tumbled into the dirt and tussled on the ground.


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[Assistant] Finally, they fell apart and settled themselves, panting beside the tree stump. Are Thampaw and Duthpaw coming too? puffed Graypaw.


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[Assistant] Nope, Firepaw replied, unable to disguise the note of triumph in his voice. They have to stay behind and guard the camp.


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[Assistant] Oh, let me tell them, begged Graypaw, I can't wait to see the looks on their faces. Me neither, Firepaw agreed.


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[Assistant] I can't believe we're going instead of them, especially after Tiger Claws saw me with Smudge today. That was just bad luck, answered Graypaw. We all caught a load of prey in the assessment. That must be what decided it. I wonder what the gathering will be like, mute Ravenpaw.


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[Assistant] It was bad luck that the great warrior had been observing him when he had met his old friend.


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[Assistant] Why couldn't he have been watching Great Paul or Raven Paul instead? In fact,


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[Assistant] It was bad luck that Tiger Claw had sent him so near the Two-Legged Place at all. Suddenly, a dark thought entered Firepaw's mind. Why had Tiger Claw sent him so near his old haunts? Had he wanted to test him? Could it be the great dark warrior?


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[Assistant] Didn't trust his loyalty to ThunderClan.


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[Assistant] My parents are gonna see it. They were the ones in the other car.


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[Assistant] Basically, what happened was there was, uh, they were talking about on this geek blog about, you know, making Spider-Man, you know, they were redoing it. So they said that maybe this new Spider-Man, since they're making it so, you know, quickly,


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[Assistant] And I was listening to it in my car, I picked up, like it was like mixing, like I was like, oh I wanna see how it sounds in a car, and I picked up a friend of mine, she got in. She was like, is this you?


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[Assistant] Being an entertainer is the only job where you can't enjoy your own stuff. Did you know that? It's the only job where you can't enjoy your own shit. Like if I made sandwiches for a living, like if I made sandwiches for a living, like if I worked at Subway or something, I made sandwiches for a living, and then I go home, and I make myself a sandwich, nobody in here is gonna be like, getting a little conceited, aren't we? Like no one cares.


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[Assistant] But like, I was talking about music. I like music a ton. And like, but the problem is like,


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[Assistant] I like weird stuff. I like weird, crazy music. Like weird people making music. And we really don't have that anymore. Like, you know, we got Lady Gaga and stuff like that, but that's, I don't think that's really weird. I feel like that's planned. Like I don't, we need weird stuff. Cause like, when, but as an adult, we're not really allowed to be weird anymore. Like the older you get,


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[Assistant] The less you can take weird stuff. That's the truth. Like you can't take weird stuff anymore. Like as a kid, like the idea of Santa Claus is really weird and fucked up.


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[Assistant] If you're like liberal and you're in your thirties, you're probably going to be liberal for the rest of your life. You know, if you're a girl and...


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[Assistant] But it's true, like, you can't take any, like, as you get older, you can't take any weird stuff. That's just the truth. Like, I, I, no.


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[Assistant] We do. We have a long history together. Like when I first moved here, when I first moved here from Atlanta, like the only thing I knew how to do and make money was to babysit because my parents, like they ran a daycare. We had a lot of foster kids. So the only thing I really knew how to do was take care of kids. So I had this job. I was supposed to pick up this kid and I was running late and I was leaving a message on the phone.


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[Assistant] And I was just like, you know, talking. And I wasn't really paying attention to where I was going. And a homeless man punched me in the face.


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[Assistant] I always have to walk in there and they ask me, like, can you walk me back? And I'm like, sure. And around the seventh time I was like, wow, every girl who comes over asks me to walk them back to their car. Like, no matter what time. And like,


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[Assistant] And we started talking about a rape that had happened in the neighborhood, and we were just like, oh, this is awful, this is so messed up, I can't believe this happened, it's so close to us. And she goes, yeah, well, if anybody ever tries to rape me, I'm just going to shit on them.


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[Assistant] I know kids pretty well, and I gotta be honest, kids are pretty fucked up anyway.


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[Assistant] Found out later that his parents were very organic and they wouldn't let him have any sugar. They wouldn't let him have any candy. He would, the only, the sweetest thing he was allowed was mints. He was just allowed to have mints. So he would steal mints by the handful.


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[Assistant] He's like, we like, we like share a split level house. He's going up the stairs with his tiny cross. He's like...


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[Assistant] The N-word still comes up in weird places. It does, like, it's strange, cause like, it doesn't really affect me.


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[Assistant] I was writing Jigga, which is the shortened form of J-Z-J-I-G-G-A, and my iPhone goes, did you mean nigga? And I went, whoa!


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[Assistant] People always want to know who can say the n-word and who can't say the n-word. You know, like people always, like I've got a lot of, you know, I've got a lot of white friends and they're all just kind of like, oh, you know, man, I wish I could say that stuff and it sounds so cool when you say it in rap song. I want to say that. It sounds cool. I'm just like, ah, it doesn't really like do anything. It's not that great, you know?


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[Assistant] Are there any terms or phrases in your act that, uh,


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[Assistant] In the entire world, I know for a fact who can say the N-word, who isn't a minority. There's one person, there's one dude, there's one dude in the entire world who can say the N-word and he's not a minority, he's not black. And that one person in the entire world who can say the N-word is Charlie Sheen.


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[Assistant] The reason Charlie Sheen gets to say the N-word is because Charlie Sheen, before all this crazy stuff happened, two years ago, got in a fight on the phone with his ex-wife, Denise Richards, and just straight up called her a nigger. Just called her, just called her the N-word. Like literally, just like, he was like, listen here, ya nigger, like really?


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[Assistant] And you know how all the light starts. He does like three, three like parts of a verse and then he gets to the end and then he holds the mic out for the N word part.


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[Assistant] Which is always good, like, you wanna learn from stuff like that. And like, one thing I did learn, I guess the biggest thing I learned was like, if, if a conversation starts with, what did you mean by that?


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[Assistant] It's weird. I mean like I, like I grew up with a bunch of like, kids. And that's basically how...


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[Assistant] I learned all about like insane stuff, like all the crazy stuff we used to do was like that's how we did it. And you know, and I want to make people happy and it's hard to find that balance sometimes because like I know I'm gross but people laugh or some people think it's kind of gross too. But I always try to make people happy like when I was a kid like we had like a bunch of kids coming and


[User] Please transcribe this text

[Assistant] We had my cousins coming over once. They were all like eight cousins. They were all coming and I wanted to do something like special for them. I wanted to do something really cool. So I used my allowance money, which took me a long time to get. I had like, I got like a dollar or two dollars like a week. So I say $20 and I went to the store and I bought all this stuff to make s'mores.


[User] Please transcribe this text

[Assistant] Take it home and like all my cousins in there and I'm like handing out the stuff. But I, I bought two for me.


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[Assistant] I find him on, he contacts me on Facebook. And he's like, hey man, what's going on? I'm like,


[User] Please transcribe this text

[Assistant] Any sugary cereals as a kid. We weren't. We just weren't allowed to have any sugary cereals. And like my mom would like get us, like the two cereals we were allowed to have was Cheerios and Kicks. And Cheerios is like cardboard doo-doo.


[User] Please transcribe this text

[Assistant] She takes the box and slides it across the table and is like, there you go.


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[Assistant] Like I said, like I grew up with a lot of foster parents and more foster kids and stuff like that.


[User] Please transcribe this text

[Assistant] Like, and like, that's how I learned about all the stuff in the world, like, sex and all that crazy stuff, cause they were talking about this crazy stuff, I'd be like, what? Like I was so like sheltered, like the parents did a good job about that.


[User] Please transcribe this text

[Assistant] Like, they did, like, and, and, it would be weird, cause like, I remember we'd have kids, I mean, like, Demarco's like my little brother, and he's adopted, but we've had him since he was little, so he's like my real brother for all intents and purposes, like, he was there since he was a baby. So like, I would mess with him like he was my little brother. Like, I'd be on the top bunk, and he'd be on the bottom bunk, and I'd be on the top, and he'd be like,


[User] Please transcribe this text

[Assistant] And he was like, you piss in my mouth I'ma bite your dick off.


[User] Please transcribe this text

[Assistant] And then for like, like for five minutes, like my little brother's like, they hit underneath him like two by fours for like five minutes. And like for ten minutes, like I hit him like some rakes.


[User] Please transcribe this text

[Assistant] Alright, well you didn't have to work that hard, it's okay. And he goes, and me and my brother look at each other,


[User] Please transcribe this text

[Assistant] Losing it. He's never lied like that before. So he's just like standing there, he's just, he can't look at my dad, he's like freaking out, shaking and stuff like that. I'm like, Terry, we're almost home free. Just hold on. We're almost there. Just hold on. We're almost there. And that's when we hear it. That's when we hear the loudest sound I've ever heard in my entire life. And it was...


[User] Please transcribe this text

[Assistant] Oh Daddy Pig, look at the mess you're in. It's only mud.


[User] Please transcribe this text

[Assistant] I have a system known as the house training triangle that will get you from point A to point B in an extremely efficient amount of time. The process is very simple, but I want you to understand the details because the details are everything. We're going to go from the crate to outside


[User] Please transcribe this text

[Assistant] Back in the house, back in the crate, complete in the triangle. Now I'm gonna talk through each and every one of these.


[User] Please transcribe this text

[Assistant] The crate. Number one, very important, crate size is key. I don't want the crate too big, because if the crate's too big, the dog can sleep on one side, walk over here, and go to the bathroom on the other.


[User] Please transcribe this text

[Assistant] The crate is too small, it's uncomfortable for the dog, and you'll have a hell of a time getting the dog in there. Uh, number two, make sure the crate is comfy, comfy bed, put some toys in there, things your dog likes, it's not punishment. You actually want the dog to enjoy their time in there.


[User] Please transcribe this text

[Assistant] Number three, crate placement. Where you place this crate is vital. You don't want to have that crate all the way in the back of the house. That way when you pull the dog out, you have to walk him 75 feet to the back door to get them to the backyard. I guarantee in that huge amount of distance, walking him to the back door, they're going to go to the bathroom.


[User] Please transcribe this text

[Assistant] Trust me, when they've been in that crate for a little while, they're going to have to use the bathroom right away. So you want to place that crate preferably by the door you're taking the dog out of. Here's how the entire process works. We're gonna back up to the night before. Before you put the dog in the crate,


[User] Please transcribe this text

[Assistant] I want you to make sure you take the dog outside, let them do their business. If they do their business outside, you reward them heavily. Give them a treat, heavy praise. From there, we're going to put them in the crate and this is where they're going to sleep at night. By the way, you're going to have a few sleepless nights because puppies cannot hold it the same way adult dogs can.


[User] Please transcribe this text

[Assistant] If they start crying at 3 or 4 o'clock in the morning, you might have to take them outside. Assuming that you lucked out and they slept all night,


[User] Please transcribe this text

[Assistant] First thing in the morning, you're gonna put a leash on them. You do not open that crate and then go find their leash. I promise you, in the first 20 seconds, if you open that crate and give them the option to go in the house, they're going to take it. Put them on a leash, you make a beeline for that outside. Guarantee within the first 20 to 30 seconds, they're gonna go pee.


[User] Please transcribe this text

[Assistant] So whatever your command might be, get busy, do your business, go potty, it's up to you. But just make sure whatever you say, you stay consistent on that exact same command. Don't be switching it up every other day. Your dog understands that that command will be connected with what they're doing.


[User] Please transcribe this text

[Assistant] The moment they go pee, I want you to have a treat in your pocket ready. The second they're done peeing,


[User] Please transcribe this text

[Assistant] reward them heavily. That's a good dog, do your business outside, all the things you say to your dog to reward them.


[User] Please transcribe this text

[Assistant] Make it positive, let them know that outside is where they're supposed to be going. First thing in the morning, there's a good chance they're gonna have to do two of their businesses, so just wait it out a few more minutes, and once they go, once again, reward, and then they're allowed to come back in the house for one hour of free time.


[User] Please transcribe this text

[Assistant] You wanna make sure the dog's free time in the house is free time in one room at a time. In other words, you don't wanna let them have free time in the entire house. Believe me, puppies, if they can't find trouble, trouble will find them. So you have to make sure this free time is observed.


[User] Please transcribe this text

[Assistant] The best way to do this if you have a house is simply shut all the doors you can and this is where baby gates or dog gates come in handy. This allows you to cut off hallways and now you can keep the dog in one room at a time, given their free time in that observed room. So after their one hour of observed free time in the house, they go


[User] Please transcribe this text

[Assistant] Into the crate, effectively completing the house training triangle.


[User] Please transcribe this text

[Assistant] Now, when you put him back in the crate, you're gonna put him back in for about 3 hours. Now you might be asking, why would I want to put the dog in the crate for 3 hours but only give him 1 hour free time in the house? The answer is very simple. You have a couple goals in mind here.


[User] Please transcribe this text

[Assistant] You wanna teach them to hold it. Just because they're in a crate doesn't mean they're not gonna go to the bathroom inside that crate. This is why the size of the crate is so important, as I mentioned earlier. If the crate's too big, they'll simply walk to one side, go to the bathroom, and go back over there and sleep.


[User] Please transcribe this text

[Assistant] But if it's just the right size, they learn to hold it. They're not gonna go to the bathroom and lie down on it.


[User] Please transcribe this text

[Assistant] Furthermore, the reason why puppies go to the bathroom so much more than adults is because they don't have the muscles to hold it. By teaching the puppy to hold it, you're teaching them two things. Number one, you're teaching them self-control. And number two, you're actually strengthening their muscles so they can hold it for longer periods of time. Believe it or not, those muscles, they get stronger very quickly.


[User] Please transcribe this text

[Assistant] And three hours one day turns into four hours the next. So after they've spent the three hours inside the crate, you want to once again repeat the process. Here's your goal.


[User] Please transcribe this text

[Assistant] Every day, you wanna add about 15 to 20 minutes free time in the house, and take away the same amount of time in the crate. Where after about a week or two,


[User] Please transcribe this text

[Assistant] You have almost no crate time left and they have hours and hours of free time in the house. Until finally one day you make the decision, you get rid of the crate altogether and at that point, your dog is now house trained.


[User] Please transcribe this text

[Assistant] Once your dog has done their business, repeat the command one more time and make sure you praise and treat them heavily right here. That way they connect the reward with doing their business.


[User] Please transcribe this text

[Assistant] From here, the next step of the house training triangle is to go back inside for free time. Okay, come on. Come on, come on, come on, come on. Come on, come on. Alright, so we just...


[User] Please transcribe this text

[Assistant] Came from outside. Oh yea, you like that, huh? She did her business.


[User] Please transcribe this text

[Assistant] Cause now, she's already gone outside and done her business, so, she should be good for about an hour, but again, this is why I say, make sure it's observed, because if you see her rearing up to go, dogs usually do get a lot of signs that they're about to go, it's pretty obvious, then you want to stop her in her tracks and hurry up and get her outside, but,


[User] Please transcribe this text

[Assistant] She should be good for the next hour, so I'm gonna let her play, do whatever she wants, this is her time.


[User] Please transcribe this text

[Assistant] In the room all by yourself, or at least not for a long period of time. You can go out, you can leave the room for a few seconds here and there, but


[User] Please transcribe this text

[Assistant] You wanna make sure most of it is observed. Oh yeah. Oh yeah.


[User] Please transcribe this text

[Assistant] When dogs eat, their systems get moving very fast. Most people that are experienced with dogs can attest to this. Typically after they eat in the first 5 to 10 minutes, their systems get going very fast and what do they have to do? They run outside and they go to the bathroom. Well the same is true with your puppy inside that crate.


[User] Please transcribe this text

[Assistant] So right after they eat, same process, put them on a leash, take them right outside, and repeat the process of rewarding them if they use the bathroom outside. And at that point, you can finish off the triangle by letting them have free time in the house and continue the triangle throughout the day.


[User] Please transcribe this text

[Assistant] What about the people that live in an apartment and use the piddle pads?


[User] Please transcribe this text

[Assistant] You do the same exact process, but there's a little minor tweak we're gonna do here. We're gonna do the same house training triangle, but instead of you taking the dog outside to the grass, you're gonna set up a pen around a piddle pad. This way the piddle pad is actually enclosed in an area where the dog can't get out.


[User] Please transcribe this text

[Assistant] You're simply going to put the dog inside of there. Wait them out. You're going to wait them out whether it takes a few minutes or even 10 minutes. Sometimes it takes a little while because the puddle pad is not like grass. It's not the natural organic material that most dogs like to go to the bathroom on. So it might take a little while.


[User] Please transcribe this text

[Assistant] Once they do their business on there, the exact same process happens. You reward them right away. You let them know this is where you want to go to the bathroom. And the moment you reward them, you can now take them out and now they can have the free time around the house. The house training triangle, whether you're doing it outside on the grass or on a pittle pad, everything works exactly the same.


[User] Please transcribe this text

[Assistant] People always ask, what do I do when the dog does use the bathroom in the house?


[User] Please transcribe this text

[Assistant] The old school way, which I've never really agreed with, was take their nose and rub them in it and yell at them and punish the hell out of them.


[User] Please transcribe this text

[Assistant] You don't need to do that anymore. There's a very simple way that I use that actually requires no verbal reprimand if you choose not to use it. All I want you to do is take a cinder block and I want you to put it right next to the area where they peter poop.


[User] Please transcribe this text

[Assistant] Wrap a leash around that cinder block and leave enough slack where they can stand up and lie down only. Attach it to their collar and leave them there for 20 to 30 minutes. That's it. This works phenomenally because most dogs do not want to hang around their pee or poop. What's the first thing they do? They get the hell away from it.


[User] Please transcribe this text

[Assistant] This is basic reverse psychology. If you're gonna poop there, you're gonna stand next to it. I'm just gonna leave you there for 20 minutes. I don't even have to say anything. Believe me, the dog gets the message.


[User] Please transcribe this text

[Assistant] Once you do this for a few days, this typically nips it in the butt. Especially if you continue doing the house training triangle. Do not stop doing the house training triangle in this process. And just a spoiler alert.


[User] Please transcribe this text

[Assistant] No matter what, even if you're following the rules every day, I guarantee you, most likely your dog will go to the bathroom in the house. It does happen. So typically, if you're combining the two, the house training triangle and using the cinderblock method,


[User] Please transcribe this text

[Assistant] That usually gets the job done in about a week or two.


[User] Please transcribe this text

[Assistant] And my couch and my two other love seats in my living room. Dogs marking their territory, it is a natural instinct. It comes from the wild animal, it comes from the wolf. But it's unacceptable in the home you live in. And it's surprisingly easy to stop.


[User] Please transcribe this text

[Assistant] Dogs typically mark on corners, corners of legs, corners of chairs. So all I want you to do here is you want to take a regular leash, just a regular throwaway nylon six foot leash. You're going to wrap that leash around the area that they mark.


[User] Please transcribe this text

[Assistant] You're only gonna leave just enough slack on the end so they can lie down and stand up. Only. What you're gonna do is you're gonna take the clip and clip it to their collar.


[User] Please transcribe this text

[Assistant] From there, you just leave him there for a good 20 to 30 minutes. If you want to reprimand lightly, you can. You can say, bad dog, don't do that again.


[User] Please transcribe this text

[Assistant] Whatever words you have to say. But the real training process is the fact that you're making them stand next to it and they can't get away from it. I promise you, within less than a week, this problem will be out the door forever.


[User] Please transcribe this text

[Assistant] Did not think of the risk she was taking when she ran through a forest after two men. They had rushed up to her while she was having a picnic at the edge of a forest with her children and tried to steal her handbag. In the struggle, the strap broke and with the bag in their possession, both men started running through the trees.


[User] Please transcribe this text

[Assistant] Mrs. Sterling got so angry that she ran after them. She was soon out of breath, but she continued to run.


[User] Please transcribe this text

[Assistant] She saw that they had sat down and were going through the contents of the bag, so she ran straight at them.


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[Assistant] Pepper? George? This is our pet parrot. She's called Polly.


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[Assistant] Pretty Polly. Ah! Pretty Polly! Wow! I am a clever parrot.


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[Assistant] Oh, don't you dare talk sexy to me. You're still on the horse then!


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[Assistant] Fizz, remember how you used to distract my dad so I could steal his booze?


[User] Please transcribe this text

[Assistant] Dentists always ask questions when it is impossible for you to answer. My dentist had just pulled out one of my teeth and had told me to rest for a while. I tried to say something, but my mouth was full of cotton wool.


[User] Please transcribe this text

[Assistant] I either nodded or made strange noises. Meanwhile.


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[Assistant] My tongue was busy searching out the hole where the tooth had been. I suddenly felt very worried but could not say anything.


[User] Please transcribe this text

[Assistant] It is George's first day. George? Are you looking forward to the playgroup?


[User] Please transcribe this text

[Assistant] Oh dear. Pepper doesn't want George to go to her playgroup.


[User] Please transcribe this text

[Assistant] Pepper is proud of her little brother George.


[User] Please transcribe this text

[Assistant] Then I cover it with earth and water it. Everything in my garden grows from tiny seeds like these.


[User] Please transcribe this text

[Assistant] And inside this apple are more seeds.


[User] Please transcribe this text

[Assistant] Yes, now it's George's turn to choose.


[User] Please transcribe this text

[Assistant] It was big enough for me when I was a boy. But it does look a bit small now.


[User] Please transcribe this text

[Assistant] And then, just like, listing all the ingredients, I was really lazy. I was like, you know what?


[User] Please transcribe this text

[Assistant] Yes please, because we're both eating this, so.


[User] Please transcribe this text

[Assistant] I'll try this out. I'm a little quiet because I'm concentrating.


[User] Please transcribe this text

[Assistant] If you make it, I would just double it or triple it so you'll have it on the side if you decide, oh it's too, it's too, uh, it's too light or it's too dry. But this is delicious the way he made it too, so.


[User] Please transcribe this text

[Assistant] Did I just say that out loud? No, I loved you, you guys, that's why I'm here. Other than the free food. And you guys, of course. Thank you. Thank you for welcoming me back.


[User] Please transcribe this text

[Assistant] No, no, it's not, it's beautiful. Like I said, I can handle a little bit of spice, but not too much where like, it kind of is painful and you don't enjoy the food anymore, so.


[User] Please transcribe this text

[Assistant] Just think of that, but with coconut so it's like creamy.


[User] Please transcribe this text

[Assistant] I'm seeing you kind of like make it more than once, like at home. Okay, I have to try to chew because...


[User] Please transcribe this text

[Assistant] That is a problem I have, so I, I noticed it in the comments, I totally do recognize that I do need to do that. Oh no, I have to watch out. That's yours, because it fell into the... What? It fell into the, the chili pit. Oh yea yea yea.


[User] Please transcribe this text

[Assistant] I'm using the ladle as my spoon, just so you know, I mean like at home it would totally be like, why, what are you doing? But I'm loving that it's welcome here.


[User] Please transcribe this text

[Assistant] Yes, I do speak it, uh, we speak it at home consistently and I wasn't actually very good at speaking Tagalog until I met him and I was, and he just like loves to speak it like that at home, so I speak it constantly. I was really terrible at first, uh, I am from Iloilo, so I do speak, uhm, I don't know what to call it, is it Hili Gainon?


[User] Please transcribe this text

[Assistant] Or, or Ilonggo, like, some people argue that hilegenon is what it's called, Ilonggo are the people, but I always knew it as Ilonggo growing up, so.


[User] Please transcribe this text

[Assistant] People talk a lot with a longer person, so.


[User] Please transcribe this text

[Assistant] But, oh, just a greeting for everybody, uh, mayong adlaw sinyong atanan, and, uh, magandang umaga or magandang araw po sinyong lahat.


[User] Please transcribe this text

[Assistant] I haven't seen Tian in a long time. I always see like his Instagram posts. I'm, I'm one of those people too that like, what do you call that, stalk you?


[User] Please transcribe this text

[Assistant] Not smiling because I have a lot of food in my mouth right now, but.


[User] Please transcribe this text

[Assistant] But for the most part, like, you do have to live, and in California, like, standard of living is going high, but not your pay, unless you go to a different job that pays more. So, that is something that I consider, uhm, now and I'm looking into.


[User] Please transcribe this text

[Assistant] They had a really good training system and like, just a very, at least in the store that I started with him at, and I'm still actually at the same location, they're very like,


[User] Please transcribe this text

[Assistant] Mmhm. Well, it depends too if they're panhandling, definitely.


[User] Please transcribe this text

[Assistant] Pretty good. My husband just got like, uhm,


[User] Please transcribe this text

[Assistant] It's been kinda tough because he works like really late and I work super early so we just miss each other. We used to like see each other for an hour a day on the weekdays.


[User] Please transcribe this text

[Assistant] Yeah, he worked two jobs for a little bit because he thought he was gonna transition to another job. I don't know, just things happen for a reason, like, if you waited out long enough and like,


[User] Please transcribe this text

[Assistant] Just work hard. Honestly, he's in a better company now and he loves it, so I'm very happy.


[User] Please transcribe this text

[Assistant] I can't really. Tina's like really good about


[User] Please transcribe this text

[Assistant] You know, I always thought estate sales meant that like,


[User] Please transcribe this text

[Assistant] Somebody had passed, and like, there's all these things that they can't get rid of, so they have the seal on the premises, but I just realized, it's exactly what he's describing.


[User] Please transcribe this text

[Assistant] I'm trying to find more food in here. I'm getting there. But I feel like I didn't eat enough.


[User] Please transcribe this text

[Assistant] There's a little bit of flavor in there, a little layer.


[User] Please transcribe this text

[Assistant] And then you get like the tang of this. So good, you guys. You have to try this at home.


[User] Please transcribe this text

[Assistant] After breakfast, I sent the children to school and then I went to the shops. It was still early when I returned home. The children were at school, my husband was at work and the house was quiet.


[User] Please transcribe this text

[Assistant] So I decided to make some meat pies.


[User] Please transcribe this text

[Assistant] In a short time, I was busy mixing butter and flour


[User] Please transcribe this text

[Assistant] And my hands were soon covered with sticky pastry. At exactly that moment the telephone rang. Nothing could have been more annoying.


[User] Please transcribe this text

[Assistant] I picked up the receiver between two sticky fingers.


[User] Please transcribe this text

[Assistant] And was dismayed when I recognized the voice of Helen Bates.


[User] Please transcribe this text

[Assistant] It took me ten minutes to persuade her to ring back later. At last I hung up the receiver. What a mess.


[User] Please transcribe this text

[Assistant] There was pastry on my fingers, on the telephone, and on the door knobs. I had no sooner got back to the kitchen


[User] Please transcribe this text

[Assistant] Then the doorbell rang, loud enough to wake the dead. This time it was the postman.


[User] Please transcribe this text

[Assistant] Equilibrium, then if you disturb them, they rock back and forth. And there's two simple examples. The standard textbook example is this mass and spring.


[User] Please transcribe this text

[Assistant] This spring has a certain natural length, which I'm showing you here. It likes to sit there.


[User] Please transcribe this text

[Assistant] But if you pull it, so the mass comes here.


[User] Please transcribe this text

[Assistant] You move it from x equal to zero to a new location x, then there is a restoring force, F, which is minus kx.


[User] Please transcribe this text

[Assistant] And that force will be equal to mass times acceleration by Newton's law.


[User] Please transcribe this text

[Assistant] And so, you're trying to solve the equation d2x over dt squared equals minus k over m times x. And we use the symbol omega squared equals k over m or omega square root of k over m.


[User] Please transcribe this text

[Assistant] And what's the solution to this equation? I think we did a lot of talking and said, look, we're looking for a function.


[User] Please transcribe this text

[Assistant] Which when differentiated twice, looks like the same function up to some constants.


[User] Please transcribe this text

[Assistant] And we know their trigonometric functions. Then we finally found


[User] Please transcribe this text

[Assistant] The answer, the most general answer looks like A cosine omega t minus phi. A is the amplitude, phi is called the phase. That tells you what your clock is doing when x is the maximum. And we can always choose phi to be zero.


[User] Please transcribe this text

[Assistant] That means when the time is zero, x will have a biggest value, a.


[User] Please transcribe this text

[Assistant] But it is a very generic situation. So I give you a second example.


[User] Please transcribe this text

[Assistant] Now we don't have a mass, we have a bar, let's say, suspended by a cable hanging from the ceiling. And it's happy the way it is, but if you come and twist it by an angle theta, give it a little twist, then it'll try to untwist itself.


[User] Please transcribe this text

[Assistant] What can be the expression for the restoring torque? When you don't do anything, it doesn't do anything.


[User] Please transcribe this text

[Assistant] So it's a function of theta that vanishes when theta is zero. If theta is not zero,


[User] Please transcribe this text

[Assistant] It will begin as some function of theta, but the leading term will be just theta. But now,


[User] Please transcribe this text

[Assistant] You can put a constant here, it'll still be proportional to theta. And you put a minus sign, for the same reason you put a minus sign here, to tell you it's a restoring torque. That means if you make theta positive, the torque will try to twist you the other way. If you make theta negative, it'll try to bring you back. So you have to find this kappa.


[User] Please transcribe this text

[Assistant] If you find this kappa, then you can say minus kappa times theta is i times d2θ over dt squared. Mathematically, that equation is identical to that, and theta then


[User] Please transcribe this text

[Assistant] It will look like some constant, you can call it A, cosine omega t minus phi, and omega now will be the ratio of this kappa to the moment of inertia.


[User] Please transcribe this text

[Assistant] That's the role played by Kappa and I. They're like K and M.


[User] Please transcribe this text

[Assistant] Now if someone tells you this is kappa, then you're done. You just stick it in and mindlessly calculate all the formulas, you can find theta, you can take derivatives and so on. Sometimes they may not tell you what kappa is. In the case of a spring,


[User] Please transcribe this text

[Assistant] They would have to give you k, or they may tell you indirectly, if I pull the spring by 9 inches, uh, it exerts a certain force, they're giving you f and they're giving you x and you can find k. But in rotation problems, the typical situation is the following.


[User] Please transcribe this text

[Assistant] Uh, the easiest problem of a pendulum. A pendulum is hanging, say a massless rod, with some mass m at the bottom.


[User] Please transcribe this text

[Assistant] So it's very happy to stay this way. If you leave it like this, it will stay this way forever. No torque, no motion. Now you come along and you disturb that by turning it by an angle theta.


[User] Please transcribe this text

[Assistant] Then the force is like this. The separation vector R from the pivot point is this. And R cross F is this.


[User] Please transcribe this text

[Assistant] Sin theta, and I told you for small angles, this can be Rf theta.


[User] Please transcribe this text

[Assistant] And r happens to be, in this problem, the length of the pendulum. So it's really minus mgl theta.


[User] Please transcribe this text

[Assistant] So you have to do some work to find theta. It wasn't just given to you in a plate. You did this piece of thinking.


[User] Please transcribe this text

[Assistant] And you, namely, you disrupt the system from equilibrium and found the restoring torque, then you stare at the formula and say, hey, this guy must be the cap I'm looking for, because that number times theta is the restoring torque.


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[Assistant] This kappa is a generic kappa that goes into whatever it is for that problem. For our problem, kappa happens to be mgl.


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[Assistant] That's something you should understand. It's not a universal.


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[Assistant] Number that's known to everybody like the spring constant of anything. In the case of Madison,


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[Assistant] This pendulum, it depends on how long the pendulum is, how big the mass is, but you can work it out and extract kappa. Downstairs you need the moment of inertia.


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[Assistant] And I remind you guys that ω is connected to what you and I would call the frequency by this 2Πf.


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[Assistant] Okay, so this is the situation. Let me give one other example. This is a homework problem, but I want to give you a hint on how to do this. Don't take a pendulum with all the mass concentrated there. Take some irregularly shaped object, a flat, planar object. You drive a nail through it there, hang it on the wall. It'll come to rest in a certain configuration.


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[Assistant] If I hang it like this on the wall. Central mass is somewhere in the body here. So I want you to think about it. I'll tell you in a second.


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[Assistant] The center of mass, I claim, will lie somewhere on this vertical line going through that point.


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[Assistant] We know all the force of gravity can be imagined to be acting here. Then if you do that separation and do the torque, then you will find this is able to exert a torque around this point. But that cannot be in equilibrium.


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[Assistant] So center of mass will always lie, will align itself. The body will swing a little bit and settle down the center of mass somewhere there.


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[Assistant] If you now disrupt the body, I don't want to draw another picture, but I'll probably fail. This is a rotated body.


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[Assistant] Between the pivot point and the center of mass.


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[Assistant] So you can read the kappa. In fact, it's just like the pendulum. In other words, as far as the torque is concerned, it's as if all the mass were sitting here. The difference will be in moment of inertia.


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[Assistant] The moment of inertia of this is not ml squared. So, don't make the mistake. All the mass is not sitting here. All the mass is sitting all over the place.


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[Assistant] It is I with respect to center of mass plus this ml squared. That's the old parallel axis theorem. So take that moment of inertia.


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[Assistant] Put that into this formula here. Take this Kappa and put it there. You'll get some frequency. That's the frequency that will oscillate. So every problem that you will ever get will look like one of these two.


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[Assistant] Either there's something moving linearly with a coordinate that you can call x.


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[Assistant] Or it's rotating or twisting by an angle you can call data.


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[Assistant] If you want to find out the frequency of vibration, you have to disturb it from equilibrium, either by pulling the mass or by twisting the cable or displacing this pendulum from its ideal position here, then finding the restoring torque. Yep?


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[Assistant] That's a very good point. His question is, if I give you a cable,


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[Assistant] And I twist the cable by some angle. How are we going to calculate restoring torque? Here is the good news. This problem is so hard, we will give it to you.


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[Assistant] In other words, that is of course an underlying answer given a cable made of some material and its torsional properties, how much of a torque you will get if you twist it by some amount. It's not something you can calculate from first principles, so they will simply have to give it to you.


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[Assistant] Okay, and such problems. The only time you'll have to find the torque on your own is in a problem like this, where I believe you know enough to figure out the torque.


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[Assistant] Okay, what you will find is, if you leave it alone, it will go to a position where there is no torque.


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[Assistant] If you move it off that position, there will be a torque, and the torque will always be proportional to the angle by which you displaced it. You read off the proportionality constant, and that's your kappa. By the way, this is not a problem. You should look at the forces too, which is pretty interesting.


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[Assistant] This body when it's hanging in its rest position has two forces on it. The nail, which is pushing up, and the weight of the body which is pushing down, and they cancel each other. The nail will keep it from falling. The nail will not keep it from swinging.


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[Assistant] Because the force of the nail acting as it does at the pivot point is unable to exert a torque.


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[Assistant] Whereas the minute you rotate the body, mg is able to exert a torque. That's why if you twist it, you'll start rattling back and forth.


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[Assistant] Alright, so what I'm going to do now is to go over, uh, more complicated oscillations using some of the techniques we learned last time.


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[Assistant] So here is the mega formula. I'm gonna give it to you guys. You have to, you're allowed to tattoo it on your face.


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[Assistant] You can carry it with you. I will allow you to bring it, but you cannot forget this formula. I think you know the formula I'm driving at. Ready?


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[Assistant] X or theta, I don't care. Let me call it theta here. It's cosine theta plus I sine theta. That's the great formula from Euler.


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[Assistant] If you take the complex conjugate of both sides, that means change every i to minus i.


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[Assistant] You will get e to the minus i theta is cosine theta minus i sine theta.


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[Assistant] You're not going to derive on the spot. It takes a lot of work. So this is something, if you tell me,


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[Assistant] What are the few things you really have to cram, that you don't want to carry in your head? Well, this is one of them.


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[Assistant] Okay, this is a formula worth memorizing, unlike formula number 92 of your text. It's not worth memorizing. This is worth memorizing. Once you got this,


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[Assistant] You should realize that in any expression involving complex numbers,


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[Assistant] That'll give you this one. That's called complex conjugation. I generally said if you have a complex number z, z star is equal to x minus iy, if z is equal to x plus iy. So in our simple example, this fellow here is z, this is the x, and this is the y.


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[Assistant] Invert the formula, you add the 2 and divide by 2, then you will find cosine theta.


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[Assistant] Is e to the iθ plus e to the minus iθ over 2.


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[Assistant] If you subtract and divide by 2i, you will find sinθ is e to the iθ minus e to the minus iθ over 2i.


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[Assistant] In other words, my claim is that this funny exponential, sum of two exponentials, is the familiar cosine. It'll do everything your cosine will do. It'll oscillate.


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[Assistant] Provided you let the exponent be complex or imaginary, you don't need trigonometric function.


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[Assistant] This is one example of grand unification. People always say, Maxwell unified this and Einstein tried to unify this. Unification means things that you thought were unrelated.


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[Assistant] Are in fact related, and there are different manifestations of the same thing.


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[Assistant] When we first discovered trigonometric functions, you know, we were drawing right angle triangles on opposite side and adjacent side. Then we discovered the exponential function. By the way, it was computed by bankers who were trying to calculate compound interest every second.


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[Assistant] The fact that those functions are related is a marvelous result, but it happens only if you go to complex numbers. This is another thing you should know.


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[Assistant] Let me just tell you that every complex number z can be written as its absolute value times some phase.


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[Assistant] In other words, if my complex number z is here, it is x plus iy, that's one way to write it. You can also write it as its absolute value, e to the iΦ, or r, e to the iΦ. r is the radial length, which also happens to be the length of the complex number.


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[Assistant] That's called the polar form of the complex number. x plus i y is the Cartesian form of the complex number.


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[Assistant] I may have called them r and theta or r and phi. I just don't remember. I'm going to use these symbols back and forth because people do use both the symbols. That's why I am sometimes calling this angle as theta and sometimes this angle as phi. But the basic idea is the same. This entity here can be written either in this form or in this form.


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[Assistant] This is something you should know. If you don't know or don't understand, you should stop and ask, because everything is built on this. So, what I'm going to do now is to go back to this rather simple equation, d2x over dt squared, equal to minus


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[Assistant] By the way, today I'm going to call this ω as ω0.


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[Assistant] It's the same guy. I'm going to call it ω0 because we will find as the hour progresses, there are going to be many ω's in the game. Two more ω's are going to come in.


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[Assistant] So we gotta be able to tell them apart. As long as there's only one omega in town, you just call it omega. If there are many, you call this omega-naught.


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[Assistant] Try to solve it for you. It's to say, turn it into a word problem.


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[Assistant] With the property that two derivatives of the function look like the function, and we raked our brains and we remembered, hey, sines and cosines are the property, one derivative is no good. Turn sine into cosine.


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[Assistant] So two derivatives bring back the function you started with, which is why the answer could be sines or cosines. But now I'm going to solve it in a different way.


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[Assistant] I know a function that repeats itself even when I differentiate it once.


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[Assistant] Namely, the function has the property that its first derivative looks like the function itself. It's obvious that its 92nd derivative will also look like the function because taking the derivative leaves the function alone except for pulling out some numbers.


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[Assistant] So why not say, I want an answer that looks like this, x equals some a in the αt.


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[Assistant] That certainly has the property that if you take two derivatives, it's going to look like e to the alpha t on the left hand side and e to the alpha t on the right hand side, and then you can cancel them and you've got yourself a solution. Do you guys remember why I didn't follow this solution for the oscillator? Why was it rejected?


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[Assistant] Ah, that's a very good point. So maybe I will take e to the minus αt. How about that? Will that give me a second derivative which is negative?


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[Assistant] You didn't fall for that, right? Because first time we'll get minus alpha, but second time we'll get plus alpha squared. That's correct. So this function is no good. Also, it doesn't look like what I want.


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[Assistant] Even without doing much mathematical physics, I know if you pull the spring, it's going to go back and forth. Whereas these functions are exponentially growing or exponentially falling, they just don't do the trick.


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[Assistant] So we're just going to take this guess and put it in the equation and see if I can get an answer that works. Okay?


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[Assistant] This is called an Ansatz. Ansatz is something we use all the time. It's a German word. I'm not sure exactly what it means, but we all use it to mean a tentative guess. That's what it is. If you're lucky, it'll work.


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[Assistant] If you're not lucky, that's fine. You move on and try another solution. So we're going to say, can a solution of this form be found? With a and alpha completely free.


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[Assistant] Maybe the equation will tell me what a and alpha should be. So let's take it, put it here.


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[Assistant] By the way, I'm going to write this equation in a form that's a little easier. x double dot is minus omega 0 squared x, where each dot is a derivative. It's just more compact that way, rather than to write all of this stuff.


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[Assistant] So let's take that guess and put it here and see what we get.


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[Assistant] I get, when I take two derivatives,


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[Assistant] Uh, you can say, do I want e to the alpha t or e to the minus alpha t? You will find it doesn't matter, so I'm going to take e to the alpha t and put it there.


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[Assistant] Now the beauty of the x function now is to take one derivative, x dot.


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[Assistant] I hope everybody knows the x star of this is a e to the alpha t, and x double dot is another alpha, a alpha squared e to the alpha t.


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[Assistant] That's the beauty of the exponential. The act of differentiation is trivial. You just multiply by the exponent, alpha. See, this being the result of taking two derivatives, uh, let me write it here now. What do I get?


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[Assistant] So I'm going to put in the guess x equals Ae to the alpha t. And what do I find? I find that it's, uh, in fact let me write the equation in a nicer way. x double dot plus omega 0 squared x has to vanish. I just brought everything to one side.


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[Assistant] Now put e to the αt, a to the αt as your guess, then you find it's α


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[Assistant] e to the alpha t plus omega zero squared a e to the alpha t has to be zero.


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[Assistant] So we know what to do. Let's group a few terms. So this means I get A


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[Assistant] No one's going to say, well, you got it by guesswork. Well, it turns out solving differential equation is only guesswork. There's no other way to solve the equation other than to make a guess, stick it in, fiddle with the parameters, see if it'll work. So we're not done yet because we want this to vanish.


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[Assistant] How many ways are there to kill this answer? You can say maybe A is zero. A is zero, you got what's called a trivial solution. Yes?


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[Assistant] Thank you very much. This one is α square plus ω0 square.


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[Assistant] Does everybody follow that? Yes, from here to here it's very clear what to do. So we cannot kill A.


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[Assistant] Yeah, yeah, yeah. I'm trying to rule out certain options I don't like.


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[Assistant] The option I don't like to get this to be 0 is to say that is 0. That's not happening. e to the alpha t is not going to vanish. Maybe it'll vanish.


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[Assistant] Uh, for some negative infinity time, but I want this to be true at all times.


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[Assistant] Equation has to be obeyed at all times, well this guy certainly is not zero at all times. The only way to fix that is to have alpha squared plus omega zero squared equal to zero. That's the only solution which is not a trivial solution.


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[Assistant] Well, that's a simple equation, right? It's a quadratic equation.


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[Assistant] Our alpha is plus or minus i omega 0.


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[Assistant] So, when we were young and we didn't know about complex numbers, we will come to this stage and we will quit and say, look, exponentials won't work, but now we are not afraid of complex exponentials, so we embrace the solution. So now I've got two solutions. By the way, what's the value of A? Think about this. If this condition is satisfied, you realize A can be whatever you like. A is completely arbitrary.


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[Assistant] So what this equation has told me is the following. Yes, there are solutions of this form.


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[Assistant] For A, you can pick any number you like. In fact, real or complex, it doesn't matter. The equation is satisfied.


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[Assistant] It's not an arbitrary number. It can be only one of two numbers, plus iω0 or minus iω0. So we got a problem now that I look for one answer, I got two. So I will write them both.


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[Assistant] Now, I think you guys can see in your head that if you take this and you put it in the equation, it works.


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[Assistant] And if you take this and put it into the equation, that also works. Because when you take two derivatives,


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[Assistant] I omega whole squared will be minus omega squared, minus I omega naught whole squared will also be minus omega naught squared, so both will work.


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[Assistant] Now we have to ask, how do I decide between that solution and that solution? It turns out that we don't have to pick.


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[Assistant] We can pick both, and I'll tell you what I mean by we can pick both.


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[Assistant] This is a very, very important property for all of you who are going into economics or engineering or chemistry.


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[Assistant] This or other disciplines which are mathematical, the property I'm going to mention of this equation is very important. So please pay attention. This is called a linear equation.


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[Assistant] A linear equation obeys a certain property called superposition. I'll have to tell you what it is. If I give you a differential equation.


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[Assistant] You know, 96 derivative of x plus 52 times the 37 derivative of x, blah, blah, blah adds up to 0. What makes it a linear equation is that throughout an equation,


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[Assistant] Either you find the function x or its derivatives, but never the squares or cubes or higher powers of x or the derivatives. Okay? The function appears to first power, not to second power. For example, if this was the equation you were trying to solve, that is not a linear equation. That's called a nonlinear equation.


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[Assistant] If you have a linear equation, that's a very, very profound consequence. And I'm going to tell you what it is, and that lies at the heart of so many things we do.


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[Assistant] So let me write down two solutions. One of them obeys x1 double dot.


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[Assistant] That's omega naught squared x1 equal to 0. Second one obeys x2 double dot plus omega naught squared x2 equal to 0.


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[Assistant] Don't even have to look at these two solutions. Take a general problem where you have a linear equation, there are two solutions. Add the two equations.


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[Assistant] On the left hand side, I get the second derivative of x1 plus the second derivative of x2. Remember, that is in fact the second derivative. Now I go back to the old notation of x1 plus x2.


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[Assistant] This has to do with the fact that the derivative of the sum is the sum of the derivatives, and the sum of the derivative is the derivative of the sum. Yep.


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[Assistant] In the second term, I get ω0 squared times x1 plus x2 equal to 0. You stare at this equation.


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[Assistant] But say in words what you found out. What you found out is that x1 satisfies the equation, x2 satisfies the equation.


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[Assistant] x1 plus x2, let's call it x plus, is x1 plus x2, also satisfies the equation. And the proof is right in front of you. And the key was, the derivative of a sum is the sum of the derivative.


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[Assistant] Now I'm going to generalize it more and say, suppose I multiply all of the first equation by A.


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[Assistant] All of the second equation by b, well that's certainly still true, right? You take z, something equal to 0, multiply both sides by a, it's still going to be 0. Now imagine adding this to this.


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[Assistant] So here is the punchline. If you give me two solutions to this equation.


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[Assistant] It looks like there are two solutions actually, there's infinite number of solutions because you can pick A and B any way you like.


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[Assistant] So linear equations typically have infinite number of solutions.


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[Assistant] And you build them up by taking a few building blocks. They're like unit vectors i and j.


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[Assistant] You can take any multiple of this unit vector, any multiple of that unit vector, and this combination will also solve the equation.


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[Assistant] Just so you don't think this is going to happen all the time, let me remind you, you don't have to write this down, but at least follow what I'm saying. Suppose this quantity here was not x1, but the square of x1, and here.


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[Assistant] Okay, you don't have to write this because this is not a linear equation. We're not interested in this, but notice this is nonlinear and you guys should be able to pick it up. It's nonlinear because I've got the square of the unknown.


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[Assistant] Now can you see, if I add these two equations, forget A and B, let them both be 1, I get x1 squared plus x2 squared. But that is not equal to


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[Assistant] So even though the derivative, second derivative of the sum is the sum of the second derivative, the sum of the squares is not the square of the sum.


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[Assistant] So for a nonlinear equation, you cannot add solutions. For a linear equation, you can combine solutions with arbitrary coefficients. That's the lesson you have learned today.


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[Assistant] So our harmonic oscillator equation is the linear equation, so feel free to combine them and get the following solution. x of t is equal to A e to the iω0t plus B e to the minus iω0t. A and B are whatever you like. Ω0 is the original root of k over f.


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[Assistant] Uh, will you be happy to take it as a solution for the mass spring system? And if not, what is it you don't like?


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[Assistant] Yes? Anybody have a view? I mean, would you take that as a good solution? Yes.


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[Assistant] Well, he's raising a point. Let me repeat his point. A and B, of course, cannot be, in general, they're arbitrary. For this mass and this spring, you can pick any A and B you like.


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[Assistant] But on a given day, when you pull it by nine centimeters and release it,


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[Assistant] The answer has to be chosen so that at t equal to 0, x becomes 9.


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[Assistant] And the velocity, let's say, was zero when you released it. So when you take the derivative of this, the velocity should vanish.


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[Assistant] The two numbers by picking these two numbers. You understand that? But that's not enough. I got another problem. Yes? Yes, that should bother you. The answer is manifestly not real. Okay? And we know x is a real function. That is not a mathematical requirement of the equation.


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[Assistant] World of complex numbers. A complex number x plus i y.


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[Assistant] has a complex conjugate x-iy and the property of real numbers


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[Assistant] Is that when you take the complex conjugate, nothing happens.


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[Assistant] Because i goes to minus i if the number was purely real.


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[Assistant] It satisfies the condition z equal to z star.


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[Assistant] So real numbers are their own complex conjugates. In general, a complex number is not its own conjugate, but if you want me to draw you a picture, that's where z is, and that's where z star is. The fellows on the x-axis have the property z is the same as z star.


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[Assistant] Z starts the reflection on the Z axis, on the X axis of Z. And therefore, if the number is real, it's its own reflection.


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[Assistant] So I'm going to demand that this solution, in addition to satisfying the basic equation, also is real.


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[Assistant] To do that, I'm going to find the complex conjugate, which is denoted by the x star of t. Now you want to conjugate everything in sight.


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[Assistant] The complex conjugate of A, I'm going to call A star. Complex conjugate of e to the i omega t is e to the minus i omega 0 t. Why? Because the i goes to minus i, omega 0 and t are real numbers. Nothing happens to them.


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[Assistant] And b becomes b star, and this becomes e to the plus i omega 0 t. And I demand that these two fellows are equal.


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[Assistant] If they're both equal, then I take this exponential and demand that those be the same.


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[Assistant] That means I demand that A be the same as B star.


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[Assistant] Because if A is the same as B star, this will go into this. And then I will demand that B is the same as A star.


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[Assistant] If these conditions are satisfied, x star will become x.


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[Assistant] So the trick is to take the function, take its complex conjugate equated to itself, and look at the consequence. Now I want to tell you that if A is equal to B star, then you don't have to worry about this as an extra condition.


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[Assistant] Because I am your complex conjugate, you are my complex conjugate. Because the way it works is, if you took A and change every i to minus i,


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[Assistant] Right? And if you took b, whatever its complex form was, change i to minus i, you get a. But if you do it one more time, you come back to where you are. In other words, for any complex number, if you start it and you start it one more time, you come back to where you are. Therefore, if a is equal to b star,


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[Assistant] Take the complex conjugate of the left hand side, you'll find A star is equal to B star star, which is B.


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[Assistant] So you don't need these two conditions, you do need A equal to B star.


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[Assistant] So in the real world, for people who want a real answer, you want to write it as A e to the i omega 0 t plus A star


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[Assistant] In other words, b is not an independent number. b has to be the complex conjugate of a. Then all of you can see at a glance that this is now real, because whatever this animal is, this is the complex conjugate of that. It's got all the i's turned into minus i. When you add them, all the i's will cancel. The answer will be real.


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[Assistant] The complex number A, which is some complex number, has a length, and it can have a phase, because every complex number can be written in this form. So, if you remember that, then you find x looks like this.


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[Assistant] Absolute value of A, e to the i omega 0 t plus phi.


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[Assistant] Plus absolute value of a, e to the minus omega zero t, plus phi.


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[Assistant] In the place of A, write the absolute value times e to the i-phi.


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[Assistant] If the i5 will combine with if the i omega t and form this exponential.


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[Assistant] Second term will be just the conjugate of the whole thing. You don't even have to think. Now, what is this function I have? I want you to think about it.


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[Assistant] Do you recognize this creature here as something familiar now? Yes? You have any idea?


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[Assistant] You remember this great identity. Where is it? Here. Uh, this one.


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[Assistant] e to the i theta plus e to the minus i theta is 2 times cosine theta.


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[Assistant] 2 times absolute value of a, cosine omega t, plus phi. And if you want, you can call 2a as another number, c.


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[Assistant] Oh, but for any complex number, you can pull certainly this number out of both.


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[Assistant] So this is a long and difficult way to get back the old answer. You got this by fiddling around and guessing and arguing physically. But I want to show you that with exponential function, you would have come to this answer anyway.


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[Assistant] We've got no problems in life. We're doing very well with cosines. Thank you. Why do you bring this exponential on us? Well, now I'm going to give you a problem.


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[Assistant] Well, you cannot talk your way out of this by just turning it into word problem. The word problem I meant,


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[Assistant] We asked a word question, find me a function whose second derivative looks like itself.


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[Assistant] And you can either start with exponentials and differentiate twice, or sines and cosines. So you don't need exponentials. But look at the following problem. This is a problem of a mass, m, force constant k, moving on a surface with friction.


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[Assistant] The minute you've got friction, you have an extra force.


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[Assistant] Friction also exerts a force, which has got some coefficient b, but it's multiplied by the velocity.


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[Assistant] We know that if you're moving to the right, the force is to the left. If you're moving to the left, the force is to the right. Frictional force is velocity dependent. So the equation you want to solve when you've got friction is really mx


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[Assistant] Can you solve this by your usual word problem? It's going to be difficult, because you want a function which when I take two derivatives,


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[Assistant] Looks like the function plus some amount of its own derivative.


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[Assistant] If you take cos omega t, it won't do it. If you take sine omega t, it won't do it.


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[Assistant] So, we can still solve it, because even this equation.


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[Assistant] You solve by the same mindless approach, which is to say, let X look like A in the αt.


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[Assistant] It has to work. You can see why, because when I take two derivatives of x, I will get α². Let me pull the a out of everything.


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[Assistant] Plus alpha gamma plus omega zero squared, e to the alpha t equal to zero.


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[Assistant] So what we learn is, yes, there are solutions of this form to this equation. Once again, A can be whatever number you like, because if A vanishes, you kill the whole solution.


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[Assistant] e to the alpha t is not going to vanish at every instant in time, so the only way is for this to vanish.


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[Assistant] That means alpha, that you put into this guess, is not any old number, but the solution to this quadratic equation, alpha squared plus alpha gamma plus omega naught squared equal to 0.


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[Assistant] So we want alpha squared plus alpha gamma is omega naught squared equal to zero. So alpha must be the root of this equation.


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[Assistant] And we all know a quadratic equation will have two roots, and we will get two solutions, and we can add them with any coefficient you like. That'll also be a solution.


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[Assistant] So let me write it down. In other words, I'm going to explicitly solve this quadratic equation.


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[Assistant] So go back to the old days, and remember that the solution of that equation will be α equals minus γ plus or minus square root of γ square minus 4ω0 square over 2.


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[Assistant] I would like to rewrite this as minus γ over 2, plus or minus square root of γ over 2, square, minus ωr².


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[Assistant] And let's call the two roots, one with a plus sign and one with a minus sign, as alpha plus and minus. This is a shorthand for this whole combination.


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[Assistant] Do you understand that if I give you the mass and the spring constant, and I give you the coefficient of friction, the number B, α± and α± are uniquely known?


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[Assistant] So you'll get two precise numbers coming out of this whole game. And your answer then to this problem will be x of t is any number a times e to the minus alpha plus t, with any number b times e to the minus alpha minus t, where alpha plus and minus are these two numbers.


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[Assistant] I want you to notice both numbers are falling exponentials.


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[Assistant] Very important, because now I'm talking about a mass where I pull the spring. There's a lot of friction and I let it go.


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[Assistant] I don't want an exponentially growing answer. That makes no sense. The x should eventually vanish. And that will in fact happen. Let's make sure you understand that. Look at these two roots. Minus gamma over 2.


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[Assistant] Plus and minus, well that is this solution, minus γ over 2 squared, minus ω0 squared. I'm going to assume in this calculation that γ over 2 is bigger than ω0. Let's do that first.