8.14: Trends in Dating, Cohabitation, and Marriage
-
- Last updated
- Save as PDF
- Lumen Learning
- Lumen Learning
Learning Outcomes
- Describe trends and norms in dating, cohabitation, and marriage in the United States
Dating
In general, traditional dating among teens and those in their early twenties has been replaced with more varied and flexible ways of getting together (and technology with social media, no doubt, plays a key role). The Friday night date with dinner and a movie that may still be enjoyed by those in their 30s gives way to less formal, more spontaneous meetings that may include several couples or a group of friends. Two people may get to know each other and go somewhere alone. How would you describe a “typical” date? Who calls, texts, or face times? Who pays? Who decides where to go? What is the purpose of the date? In general, greater planning is required for people who have additional family and work responsibilities.
Dating and the Internet
The ways people are finding love has changed with the advent of the Internet. In a poll, 49% of all American adults reported that either themselves or someone they knew had dated a person they met online (Madden & Lenhart, 2006). As Finkel and colleagues (2007) found, social networking sites, and the Internet generally, perform three important tasks. Specifically, sites provide individuals with access to a database of other individuals who are interested in meeting someone. Dating sites generally reduce issues of proximity, as individuals do not have to be close in proximity to meet. Also, they provide a medium in which individuals can communicate with others. Finally, some Internet dating websites advertise special matching strategies, based on factors such as personality, hobbies, and interests, to identify the “perfect match” for people looking for love online. In general, scientific questions about the effectiveness of Internet matching or online dating compared to face-to-face dating remain to be answered.
It is important to note that social networking sites have opened the doors for many to meet people that they might not have ever had the opportunity to meet; unfortunately, it now appears that the social networking sites can be forums for unsuspecting people to be duped. In 2010 a documentary, Catfish, focused on the personal experience of a man who met a woman online and carried on an emotional relationship with this person for months. As he later came to discover, though, the person he thought he was talking and writing with did not exist. As Dr. Aaron Ben-Zeév stated, online relationships leave room for deception; thus, people have to be cautious.
Cohabitation
Cohabitation is an arrangement where two people who are not married live together. They often involve a romantic or sexually intimate relationship on a long-term or permanent basis. Such arrangements have become increasingly common in Western countries during the past few decades, being led by changing social views, especially regarding marriage, gender roles and religion. Today, cohabitation is a common pattern among people in the Western world. In Europe, the Scandinavian countries have been the first to start this leading trend, although many countries have since followed. Mediterranean Europe has traditionally been very conservative, with religion playing a strong role. Until the mid-1990s, cohabitation levels remained low in this region, but have since increased. Cohabitation is common in many countries, with the Scandinavian nations of Iceland, Sweden, and Norway reporting the highest percentages, and more traditional countries like India, China, and Japan reporting low percentages (DeRose, 2011).
In countries where cohabitation is increasingly common, there has been speculation as to whether or not cohabitation is now part of the natural developmental progression of romantic relationships: dating and courtship, then cohabitation, engagement, and finally marriage. Though, while many cohabitating arrangements ultimately lead to marriage, many do not.
How prevalent is cohabitation today in the United States? According to the U.S. Census Bureau (2018), cohabitation has been increasing, while marriage has been decreasing in young adulthood. As seen in the graph below, over the past 50 years, the percentage of 18-24 year olds in the U.S. living with an unmarried partner has gone from 0.1 percent to 9.4 percent, while living with a spouse has gone from 39.2 percent to 7 percent. More 18-24 year olds live with an unmarried partner now than with a married partner.
While the percent living with a spouse is still higher than the percent living with an unmarried partner among 25 to 34-year-olds today, the next graph clearly shows a similar pattern of decline in marriage and increase in cohabitation over the last five decades. The percent living with a spouse in this age group today is only half of what it was in 1968 (40.3 percent vs. 81.5 percent), while the percent living with an unmarried partner rose from 0.2 percent to 14.8 percent in this age group. Another way to look at some of the data is that only 30% of today’s 18 to 34-year-olds in the U.S. are married, compared with almost double that, 59 percent forty years ago (1978). The marriage rates for less-educated young adults (who tend to have lower income) have fallen at faster rates than those of better educated young adults since the 1970s. Past and present economic climate are key factors; perhaps more couples are waiting until they can afford to get married, financially. Gurrentz (2018) does caution that there are limitations of the measures of cohabitation, particularly in the past. [1]
How long do cohabiting relationships last?
Cohabitation tends to last longer in European countries than in the United States. Half of cohabiting relationships in the U. S. end within a year; only 10 percent last more than 5 years. These short-term cohabiting relationships are more characteristics of people in their early 20s. Many of these couples eventually marry. Those who cohabit more than five years tend to be older and more committed to the relationship. Cohabitation may be preferable to marriage for a number of reasons. For partners over 65, cohabitation is preferable to marriage for practical reasons. For many of them, marriage would result in a loss of Social Security benefits and consequently is not an option. Others may believe that their relationship is more satisfying because they are not bound by marriage.
Think it Over
Do you think that you will cohabitate before marriage? Or did you cohabitate? Why or why not? Does your culture play a role in your decision? Does what you learned in this module change your thoughts on this practice?
Same-Sex Couples
As of 2019, same-sex marriage is legal in 28 countries, and counting. Many other countries either recognize same-sex couples for the purpose of immigration, grant rights for domestic partnerships or grant common law marriage status to same-sex couples.
Same-sex couples struggle with concerns such as the division of household tasks, finances, sex, and friendships as do heterosexual couples. One difference between same-sex and heterosexual couples, however, is that same-sex couples have to live with the added stress that comes from social disapproval and discrimination. And continued contact with an ex-partner may be more likely among homosexuals and bisexuals because of the closeness of the circle of friends and acquaintances.
The number of adults who remain single has increased dramatically in the last 30 years. We have more people who never marry, more widows and more divorcees driving up the number of singles. Singles represent about 25 percent of American households. Singlehood has become a more acceptable lifestyle than it was in the past and many singles are very happy with their status. Whether or not a single person is happy depends on the circumstances of their remaining single.
Stein’s Typology of Singles
Many of the research findings about singles reveal that they are not all alike. Happiness with one’s status depends on whether the person is single by choice and whether the situation is permanent. Let’s look at Stein’s (1981) four categories of singles for a better understanding of this.
- Voluntary temporary singles : These are younger people who have never been married and divorced people who are postponing marriage and remarriage. They may be more involved in careers or getting an education or just wanting to have fun without making a commitment to any one person. They are not quite ready for that kind of relationship. These people tend to report being very happy with their single status.
- Voluntary permanent singles : These individuals do not want to marry and aren’t intending to marry. This might include cohabiting couples who don’t want to marry, priests, nuns, or others who are not considering marriage. Again, this group is typically single by choice and understandably more contented with this decision.
- Involuntary temporary : These are people who are actively seeking mates. They hope to marry or remarry and may be involved in going on blind dates, seeking a partner on the internet or placing “getting personal” aids in search of a mate. They tend to be more anxious about being single.
- Involuntary permanent : These are older divorced, widowed, or never-married people who wanted to marry but have not found a mate and are coming to accept singlehood as a probable permanent situation. Some are bitter about not having married while others are more accepting of how their life has developed.
Engagement and Marriage
Most people will marry in their lifetime. In the majority of countries, 80% of men and women have been married by the age of 49 (United Nations, 2013). Despite how common marriage remains, it has undergone some interesting shifts in recent times. Around the world, people are tending to get married later in life or, increasingly, not at all. People in more developed countries (e.g., Nordic and Western Europe), for instance, marry later in life—at an average age of 30 years. This is very different than, for example, the economically developing country of Afghanistan, which ha s one of the lowest average-age statistics for marriage—at 20.2 years (United Nations, 2013). Another shift seen around the world is a gender gap in terms of age when people get married. In every country, men marry later than women. Since the 1970’s, the average age of marriage has increased for both women and men.
As illustrated, the courtship process can vary greatly around the world. So too can an engagement—a formal agreement to get married. Some of these differences are small, such as on which hand an engagement ring is worn. In many countries, it is worn on the left, but in Russia, Germany, Norway, and India, women wear their ring on their right. There are also more overt differences, such as who makes the proposal. In India and Pakistan, it is not uncommon for the family of the groom to propose to the family of the bride, with little to no involvement from the bride and groom themselves. In most Western industrialized countries, it is traditional for the male to propose to the female. What types of engagement traditions, practices, and rituals are common where you are from? How are they changing?
Contemporary young adults in the United States are waiting longer than before to marry. The median age of entering marriage in the United States is 27 for women and 29 for men (U.S. Bureau of the Census, 2011). This trend in delays of young adults taking on adult roles and responsibilities is discussed in our earlier section about “emerging adulthood” or the transition from adolescence to adulthood identified by Arnett (2000).
A fair exchange
Social exchange theory suggests that people try to maximize rewards and minimize costs in social relationships. Each person entering the marriage market comes equipped with assets and liabilities or a certain amount of social currency with which to attract a prospective mate. For men, assets might include earning potential and status while for women, assets might include physical attractiveness and youth.
Customers in the “marriage market” do not look for a “good deal,” however. Rather, most look for a relationship that is mutually beneficial or equitable. One of the reasons for this is because most a relationship in which one partner has far more assets than the other will result if power disparities and a difference in the level of commitment from each partner. According to Waller’s principle of least interest, the partner who has the most to lose without the relationship (or is the most dependent on the relationship) will have the least amount of power and is in danger of being exploited. A greater balance of power, then, may add stability to the relationship.
Societies specify through both formal and informal rules who is an appropriate mate. Consequently, mate selection is not completely left to the individual. Rules of endogamy indicate within which groups we should marry. For example, many cultures specify that people marry within their own race, social class, age group, or religion. These rules encourage homogamy or marriage between people who share social characteristics (the opposite is known as heterogamy ). The majority of marriages in the U.S. are homogamous with respect to race, social class, age and to a lesser extent, religion.
In a comparison of educational homogamy in 55 countries, Smits (2003) found strong support for higher-educated people marrying other highly educated people. As such, education appears to be a strong filter people use to help them select a mate. The most common filters we use—or, put another way, the characteristics we focus on most in potential mates—are age, race, social status, and religion (Regan, 2008). Other filters we use include compatibility, physical attractiveness (we tend to pick people who are as attractive as we are), and proximity (for practical reasons, we often pick people close to us) (Klenke-Hamel & Janda, 1980).
According to the filter theory of mate selection, the pool of eligible partners becomes narrower as it passes through filters used to eliminate members of the pool (Kerckhoff & Davis, 1962). One such filter is propinquity or geographic proximity. Mate selection in the United States typically involves meeting eligible partners face to face. Those with whom one does not come into contact are simply not contenders (though this has been changing with the Internet). Race and ethnicity is another filter used to eliminate partners. Although interracial dating has increased in recent years and interracial marriage rates are higher than before, interracial marriage still represents only 5.4 percent of all marriages in the United States. Physical appearance is another feature considered when selecting a mate. Age, social class, and religion are also criteria used to narrow the field of eligibles. Thus, the field of eligibles becomes significantly smaller before those things we are most conscious of such as preferences, values, goals, and interests, are even considered.
Arranged Marriages
In some cultures, however, it is not uncommon for the families of young people to do the work of finding a mate for them. For example, the Shanghai Marriage Market refers to the People’s Park in Shanghai, China—a place where parents of unmarried adults meet on weekends to trade information about their children in attempts to find suitable spouses for them (Bolsover, 2011). In India, the marriage market refers to the use of marriage brokers or marriage bureaus to pair eligible singles together (Trivedi, 2013). To many Westerners, the idea of arranged marriage can seem puzzling. It can appear to take the romance out of the equation and violate values about personal freedom. On the other hand, some people in favor of arranged marriage argue that parents are able to make more mature decisions than young people.
While such intrusions may seem inappropriate based on your upbringing, for many people of the world such help is expected, even appreciated. In India for example, “parental arranged marriages are largely preferred to other forms of marital choices” (Ramsheena & Gundemeda, 2015, p. 138). Of course, one’s religious and social caste plays a role in determining how involved family may be.
Glossary
- cohabitation
- an arrangement where two people who have not married live together
- filter theory of mate selection
- the pool of eligible partners becomes narrower as it passes through filters used to eliminate members of the pool
- homogamy
- marriage between people who share social characteristics
- heterogamy
- marriage between people who do not share social characteristics
- social exchange theory
- people try to maximize rewards and minimize costs in social relationships
- Gurrentz, B. (2018, November 15). Living with an unmarried partner now common for young adults. https://www.census.gov/library/stories/2018/11/cohabitation-is-up-marriage-is-down-for-young-adults.html<EMAIL_ADDRESS>Contributors and Attributions
- Modification, adaptation, and original content. Authored by : Margaret Clark-Plaskie for Lumen Learning. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Psyc 200 Lifespan Psychology . Authored by : Laura Overstreet . Located at : http://opencourselibrary.org/econ-201/ . License : CC BY: Attribution
- Section on Love and the Internet. Authored by : Debi Brannan and Cynthia D. Mohr . Provided by : Western Oregon University, Portland State University. Located at : https://nobaproject.com/modules/love-friendship-and-social-support . Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- https://en.Wikipedia.org/wiki/Cohabitation . Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Cohabitation . License : CC BY-SA: Attribution-ShareAlike
- The Family; courtship and marriage. Authored by : Joel A. Muraco . Provided by : University of Wisconsin, Green Bay. Located at : https://nobaproject.com/modules/the-family . Project : The Noba Project. License : CC BY-SA: Attribution-ShareAlike
- Living with an Unmarried Partner Now Common for Young Adults Images . Authored by : Benjamin Gurrentz. Provided by : United States Census Bureau. Located at : https://www.census.gov/library/stories/2018/11/cohabitaiton-is-up-marriage-is-down-for-young-adults.html . License : All Rights Reserved


1.2: Addition and Multiplication of Matrices
View Addition & Multiplication of Matrices on YouTube
Matrices can be added and multiplied. Matrices can be added only if they have the same dimension, and addition proceeds element by element. For example,
\[\left(\begin{array}{cc}a&b\\c&d\end{array}\right)+\left(\begin{array}{cc}e&f\\g&h\end{array}\right)=\left(\begin{array}{cc}a+e&b+f\\c+g&d+h\end{array}\right).\nonumber \]
Multiplication of a matrix by a scalar is also easy. The rule is to just multiply every element of the matrix by the scalar. The \(2\)-by-\(2\) case is illustrated a
\[k\left(\begin{array}{cc}a&b\\c&d\end{array}\right)=\left(\begin{array}{cc}ka&kb\\kc&kd\end{array}\right).\nonumber \]
Matrix multiplication, however, is more complicated. Matrices (excluding the scalar) can be multiplied only if the number of columns of the left matrix equals the number of rows of the right matrix. In other words, an \(m\)-by-\(n\) matrix on the left can be multiplied by an \(n\)-by-\(k\) matrix on the right. The resulting matrix will be \(m\)-by-\(k\). We can illustrate matrix multiplication using two \(2\)-by-\(2\) matrices, writing
\[\left(\begin{array}{cc}a&b\\c&d\end{array}\right)\left(\begin{array}{cc}e&f\\g&h\end{array}\right)=\left(\begin{array}{cc}ae+bg&af+bh\\ce+dg&cf+dh\end{array}\right).\nonumber \]
The standard way to multiply matrices is as follows. The first row of the left matrix is multiplied against and summed with the first column of the right matrix to obtain the element in the first row and first column of the product matrix. Next, the first row is multiplied against and summed with the second column; then the second row is multiplied against and summed with the first column; and finally the second row is multiplied against and summed with the second column.
In general, a particular element in the resulting product matrix, say in row \(k\) and column \(l\), is obtained by multiplying and summing the elements in row \(k\) of the left matrix with the elements in column \(l\) of the right matrix.
Consider the Fibonacci \(\text{Q}\)-matrix given by
\[\text{Q}=\left(\begin{array}{cc}1&1\\1&0\end{array}\right)\nonumber \]
Determine \(\text{Q}^n\) in terms of the Fibonacci numbers.
Solution
The famous Fibonacci sequence is \(1,\: 1,\: 2,\: 3,\: 5,\: 8,\: 13,\ldots\), where each number in the sequence is the sum of the preceeding two numbers, and the first two numbers are set equal to one. With \(F_n\) the \(n\)th Fibonacci number, the mathematical definition is
\[F_{n+1}=F_n+F_{n-1},\quad F_1=F_2=1,\nonumber \]
and we may define \(F_0=0\) so that \(F_0+F_1=F_2\).
Notice what happens when a matrix is multiplied by \(\text{Q}\) on the left:
\[\left(\begin{array}{cc}1&1\\1&0\end{array}\right)\left(\begin{array}{cc}a&b\\c&d\end{array}\right)=\left(\begin{array}{cc}a+c&b+d\\a&c\end{array}\right).\nonumber \]
The first row is replaced by the sum of the first and second rows, and the second row is replaced by the first row. Using the Fibonacci numbers, we can cleverly write the Fibonacci \(\text{Q}\)-matrix as
\[\text{Q}=\left(\begin{array}{cc}1&1\\1&0\end{array}\right)=\left(\begin{array}{cc}F_2&F_1\\F_1&F_0\end{array}\right);\nonumber \]
and then using the Fibonacci recursion relation we have
\[\text{Q}^2=\left(\begin{array}{cc}F_3&F_2\\F_2&F_1\end{array}\right),\quad\text{Q}^3=\left(\begin{array}{cc}F_4&F_3\\F_3&F_2\end{array}\right).\nonumber \]
More generally,
\[\text{Q}^n=\left(\begin{array}{cc}F_{n+1}&F_n \\ F_n&F_{n-1}\end{array}\right).\nonumber \]


3.6: Communication Channels
-
- Last updated
- Save as PDF
- Anonymous
- LibreTexts
Learning Objectives
- Understand how communication channels affect communication.
- Recognize different communication directions within organizations.
The channel, or medium, used to communicate a message affects how accurately the message will be received. Verbal, written, and nonverbal communications have different strengths and weaknesses. In business, the decision to communicate verbally or in written form can be a powerful one. In addition, a smart manager is aware of the nonverbal messages conveyed by either type of communication—as noted earlier, only 7% of verbal communication comes from the words themselves.
Information Richness
Channels vary in their information richness . Information-rich channels convey more nonverbal information. As you may be able to guess from our earlier discussion of verbal and written communications, verbal communications are richer than written ones. Research shows that effective managers tend to use more information-rich communication channels than less effective managers (Allen & Griffeth, 1997; Fulk & Boyd, 1991; Yater & Orlikowski, 1992). The figure below illustrates the information richness of different information channels.
Adapted from information in Daft, R. L., & Lenge, R. H. (1984). Information richness: A new approach to managerial behavior and organizational design. In B. Staw & L. Cummings (Eds.), Research in organizational behavior (Vol. 6, pp. 191–233). Greenwich, CT: JAI Press; and Lengel, R. H., & Daft, D. L. (1988). The selection of communication media as an executive skill. Academy of Management Executive , 11 , 225–232.
Like face-to-face and telephone conversation, videoconferencing has high information richness because Receivers and Senders can see or hear beyond just the words—they can see the Sender’s body language or hear the tone of their voice. Handheld devices, blogs, and written letters and memos offer medium-rich channels because they convey words and pictures/photos. Formal written documents, such as legal documents, and spreadsheets, such as the division’s budget, convey the least richness because the format is often rigid and standardized. As a result, nuance is lost.
In business, the decision to communicate verbally or in written form can be powerful. In addition, a smart manager is aware of the nonverbal messages conveyed by either type of communication—as noted earlier, only 7% of a verbal communication comes from the words themselves.
When determining whether to communicate verbally or in writing, ask yourself: Do I want to convey facts or feelings ? Verbal communications are a better way to convey feelings. Written communications do a better job of conveying facts.
Picture a manager making a speech to a team of 20 employees. The manager is speaking at a normal pace. The employees appear interested. But how much information is being transmitted? Not as much as the speaker believes! Humans listen much faster than they speak. The average public speaker communicates at a speed of about 125 words a minute. And that pace sounds fine to the audience. (In fact, anything faster than that probably would sound weird. To put that figure in perspective, someone having an excited conversation speaks at about 150 words a minute.) On the basis of these numbers, we could assume that the employees have more than enough time to take in each word the manager delivers. And that’s the problem. The average person in the audience can hear 400–500 words a minute (Lee & Hatesohl, 2008). The audience has more than enough time to hear. As a result, they will each be processing many thoughts of their own, on totally different subjects, while the manager is speaking. As this example demonstrates, oral communication is an inherently flawed medium for conveying specific facts. Listeners’ minds wander! It’s nothing personal—in fact, it’s totally physical. In business, once we understand this fact, we can make more intelligent communication choices based on the kind of information we want to convey.
The key to effective communication is to match the communication channel with the goal of the communication (Barry & Fulmer, 2004). For example, written media may be a better choice when the Sender wants a record of the content, has less urgency for a response, is physically separated from the Receiver, doesn’t require a lot of feedback from the Receiver, or the Message is complicated and may take some time to understand. Oral communication, however, makes more sense when the Sender is conveying a sensitive or emotional Message, needs feedback immediately, and does not need a permanent record of the conversation. Use the guide provided for deciding when to use written versus verbal communication.
use written forms when conveying facts, need a record, not urgen, do not need immediate feedback and ideas are complex. Use verbal communication when conveying emotions, message is ephemeral, time urgent, ideas are simple
Business Use of E-Mail
The growth of e-mail has been spectacular, but it has also created challenges in managing information and an ever-increasing speed of doing business. Over 100 million adults in the United States use e-mail regularly (at least once a day) (Taylor, 2002).  That makes e-mail the second most popular medium of communication worldwide, second only to voice. A 2005 study estimated that less than 1% of all written human communications even reached paper—and we can imagine that this percentage has gone down even further since then (Isom, 2005). To combat the overuse of e-mail, companies such as Intel have even instituted “no e-mail Fridays” where all communication is done via other communication channels. Learning to be more effective in your e-mail communications is an important skill. To learn more, check out the business e-mail do’s and don’ts.
Business E-Mail Do’s and Don’ts
- DON’T send or forward chain e-mails.
- DON’T put anything in an e-mail that you don’t want the world to see.
- DON’T write a Message in capital letters—this is the equivalent of SHOUTING.
- DON’T routinely “cc” everyone all the time. Reducing inbox clutter is a great way to increase communication.
- DON’T hit Send until you spell-check your e-mail.
- DO use a subject line that summarizes your Message, adjusting it as the Message changes over time.
- DO make your request in the first line of your e-mail. (And if that’s all you need to say, stop there!)
- DO end your e-mail with a brief sign-off such as, “Thank you,” followed by your name and contact information.
- DO think of a work e-mail as a binding communication.
- DO let others know if you’ve received an e-mail in error.
Source : Adapted from information in Leland, K., & Bailey, K. (2000). Customer service for dummies . New York: Wiley; Information Technology Services (1997). Top 10 email dos and top ten email don’ts. Retrieved July 1, 2008, from the University of Illinois at Chicago Medical Center Web site: www.uic.edu/hsc/uicmc/its/customers/email-tips.htm; Kawasaki, G. (2006, February 3). The effective emailer. Retrieved July 1, 2008, from How to Change the World Web site: blog.guykawasaki.com/2006/02/the_effective_e.html.
An important, although often ignored, rule when communicating emotional information is that e-mail’s lack of richness can be your loss. As we saw in the chart above, e-mail is a medium-rich channel. It can convey facts quickly. But when it comes to emotion, e-mail’s flaws make it far less desirable a choice than oral communication—the 55% of nonverbal cues that make a conversation comprehensible to a listener are missing. E-mail readers don’t pick up on sarcasm and other tonal aspects of writing as much as the writer believes they will, researchers note in a recent study (Kruger, 2005).
The Sender may believe she has included these emotional signifiers in her Message. But, with words alone, those signifiers are not there. This gap between the form and content of e-mail inspired the rise of emoticons—symbols that offer clues to the emotional side of the words in each Message. Generally speaking, however, emoticons are not considered professional in business communication.
You might feel uncomfortable conveying an emotionally laden message verbally, especially when the message contains unwanted news. Sending an e-mail to your staff that there will be no bonuses this year may seem easier than breaking the bad news face-to-face, but that doesn’t mean that e-mail is an effective or appropriate way to deliver this kind of news. When the Message is emotional, the Sender should use verbal communication. Indeed, a good rule of thumb is that the more emotionally laden messages require more thought in the choice of channel and how they are communicated.
Direction of Communication Within Organizations
Information can move horizontally, from a Sender to a Receiver, as we’ve seen. It can also move vertically, down from top management or up from the front line. Information can also move diagonally between and among levels of an organization, such as a Message from a customer service representative up to a manager in the manufacturing department, or a Message from the chief financial officer sent down to all department heads.
There is a chance for these arrows to go awry, of course. As Mihaly Csikszentmihalyi, author of best-selling books such as Flow , has noted, “In large organizations the dilution of information as it passes up and down the hierarchy, and horizontally across departments, can undermine the effort to focus on common goals.” Managers need to keep this in mind when they make organization design decisions as part of the organizing function.
The organizational status of the Sender can affect the Receiver’s attentiveness to the Message. For example, consider: A senior manager sends a memo to a production supervisor. The supervisor, who has a lower status within the organization, is likely to pay close attention to the Message. The same information, conveyed in the opposite direction, however, might not get the attention it deserves. The Message would be filtered by the senior manager’s perception of priorities and urgencies.
Requests are just one kind of communication in business. Other communications, both verbal or written, may seek, give, or exchange information. Research shows that frequent communications with one’s supervisor is related to better job performance ratings and overall organizational performance (Snyder & Morris, 1984; Kacmar, et. al., 2003). Research also shows that lateral communication done between peers can influence important organizational outcomes such as turnover (Krackhardt & Porter, 1986).
External Communications
External communications deliver specific business messages to individuals outside an organization. They may announce changes in staff or strategy, earnings, and more. The goal of an external communication is to create a specific Message that the Receiver will understand and share with others. Examples of external communications include the following:
Press Releases
Public relations professionals create external communications about a client’s product, services or practices for specific Receivers. These Receivers, it is hoped, will share the Message with others. In time, as the Message is passed along, it should appear to be independent of The Sender, creating the illusion of an independently generated consumer trend, public opinion, and so on.
The Message of a public relations effort may be b2b (business to business), b2c (business to consumer), or media related. The Message can take different forms. Press releases try to convey a newsworthy message, real or manufactured. It may be constructed like a news item, inviting editors or reporters to reprint the Message in part, or as a whole, with or without acknowledgment of the Sender’s identity. Public relations campaigns create Messages over time, through contests, special events, trade shows, and media interviews in addition to press releases.
Ads
Advertising places external business Messages before target Receivers through media buys. A media buy is a fee that is paid to a television network, Web site, or magazine by an advertiser for an on-air, site, or publication ad. The fee is based on the perceived value of the audience who watches, reads, or frequents the space where the ad will appear.
In recent years, Receivers have begun to filter advertiser’s Messages, a phenomenon that is perceived to be the result of the large amount of ads the average person sees each day and a growing level of consumer wariness of paid Messaging. Advertisers, in turn, are trying to create alternative forms of advertising that Receivers won’t filter. The advertorial is one example of an external communication that combines the look of an article with the focused Message of an ad. Product placements in videos, movies, and games are other ways that advertisers strive to reach Receivers with commercial Messages.
Web Pages
A Web page’s external communication can combine elements of public relations, advertising, and editorial content, reaching Receivers on multiple levels and in multiple ways. Banner ads, blogs, and advertiser-driven “click-through” areas are just a few of the elements that allow a business to deliver a Message to a Receiver online. The perceived flexibility of online communications can impart a less formal (and, therefore, more believable) quality to an external communication. A Message relayed in a daily blog post will reach a Receiver differently than if it is delivered in an annual report, for example. The popularity and power of blogs is growing, with 11% of Fortune 500 companies having official blogs (up from 4% in 2005). In fact, blogs have become so important to some companies as Coca-Cola, Kodak, and Marriott that they have created official positions within their organizations titled “Chief Blogging Officer (Workforce, 2008).”
The “real-time” quality of Web communications may appeal to Receivers who might filter out a traditional ad and public relations message because of its “prefab” quality. Despite their “spontaneous” feel, many online pages can be revisited in perpetuity. For this reason, clear and accurate external communications are as vital for online use as they are in traditional media.
Customer Communications
Customer communications can include letters, catalogs, direct mail, e-mails, text messages, and telemarketing messages. Some Receivers automatically filter bulk messages like these. Others will be receptive. The key to a successful external communication to customers is to convey a business message in a personally compelling way—dramatic news, a money-saving coupon, and so forth.
Key Takeaway
Different communication channels are more or less effective at transmitting different kinds of information. Some types of communication are information rich while others are medium rich. In addition, communications flow in different directions within organizations. A major internal communication channel is e-mail, which is convenient but needs to be handled carefuly. External communication channels include PR/press releases, ads, Web pages, and customer communications such as letters and catalogs.
Exercises
- How could you use your knowledge of communication richness to be more effective in your own communications?
- What are the three biggest advantages and disadvantages you see regarding technology and communications?
- Explain the difference between internal and external communications in an organization, giving examples of each.
References
Allen, D. G., & Griffeth, R. W. (1997). Vertical and lateral information processing.
Barry, B., & Fulmer, I. S. (2004). The medium and the Message: The adaptive use of communication media in dyadic influence . Academy of Management Review , 29 , 272–292.
CNET, 60 Billion emails sent daily worldwide. (2006, April 26). Retrieved July 2, 2008, from CNET.UK:.
Fulk, J., & Boyd, B. (1991). Emerging theories of communication in organizations. Journal of Management , 17 , 407–446.
Isom, David. www.sims.berkeley.edu/researc...info/index.htm, as cited in David K. Isom. (2005, October 19). Electronic discovery: New power, new risks. Retrieved July 2, 2008, from utahbar.org/barjournal2000/html/november_2003_2.html.
Kacmar, K. M., Witt, L. A., Zivnuska, S., & Guly, S. M. (2003). The interactive effect of leader-member exchange and communication frequency on performance ratings. Journal of Applied Psychology , 88 , 764–772.
Krackhardt, D., & Porter, L. W. (1986). The snowball effect: Turnover embedded in communication networks. Journal of Applied Psychology , 71 , 50–55.
Kruger, J. (2005). Egocentrism over email: Can we communicate as well as we think? Journal of Personality and Social Psychology , 89 , 925–936.
Lee, D., & Hatesohl, D. Listening: Our most used communication skill. University of Missouri. Retrieved July 2, 2008, from extension.missouri.edu/explore/comm/cm0150.htm.
Snyder, R. A., & Morris, J. H. (1984). Organizational communication and performance. Journal of Applied Psychology , 69 , 461–465.
Taylor, C. (2002, June 10). 12 steps for email addicts. Time.com . Retrieved July 2, 2008, from www.time.com/time/magazine/article/0,9171,1002621,00.html.
Workforce, Chief blogging officer title catching on with corporations. (2008, May 1). Workforce Management News in Brief . Retrieved July 2, 2008, from http://www.workforce.com/section/00/article/25/50/77.html .
Yates, J., & Orlikowski, W. J. (1992). Genres of organizational communication: A structurational approach to studying communication and media. Academy of Management Review , 17 , 299–326.


7.4: Policies Affecting Drug Approval, Supply, and Cost
By the end of this section, you should be able to:
- Examine the role of the FDA in protecting public health.
- Understand the global drug manufacturing supply chain.
- Examine factors contributing to U.S. pharmaceutical costs being higher than those of other countries and their implications.
As discussed, the FDA is a regulatory body under the HHS umbrella. The FDA has broad regulatory authority and is responsible for protecting public health by ensuring the safety and efficacy of the food supply and all medical drugs, products, and devices (FDA, 2023). Table 7.8 lists examples of products over which the FDA has authority in eight regulatory areas.
| Regulatory Areas | Products over Which the FDA Has Authority |
|---|---|
| Foods |
|
| Drugs |
|
| Biologics |
|
| Medical devices |
|
| Electronic radiation products |
|
| Cosmetics |
|
| Veterinary products |
|
| Tobacco products |
|
As a regulatory body, the FDA has specific policies and regulations aimed at protecting the health and well-being of the American public. The agency develops rules and regulations based on evidence-based processes and through the input of other government agencies and subject matter experts. The FDA regulations are then published in the Federal Register , the U.S. government’s official publication for notifying the public of agency actions. FDA regulations are either required or authorized by statute.
The rules established by the FDA may come through the creation of laws by Congress, presidential executive orders, or regulations established within the FDA. Before a new drug is approved for public consumption, for example, the drug is subject to a stringent testing and research process to identify potential harm to the affected population. Once the food, drug, or other item is approved, it is then made available for public consumption.
One of the most recent FDA actions was the approval of the COVID-19 vaccine (FDA, n.d.). Although the process of approving a drug or other material for human and animal consumption generally takes years, the approval of the COVID-19 vaccine was expedited due to the nature of the COVID-19 pandemic and the need to limit new cases of the disease (FDA, n.d.). The FDA and drug makers worked at an accelerated pace to complete the required testing on the new vaccines before they were released to the public to ensure their safety and efficacy (Figure 7.5).
This video provides a brief overview of the process the FDA follows to approve new drugs.
Watch this video, and then respond to the following questions.
- What considerations are involved in the decision to test a new drug on human subjects?
- What are the three phases of clinical trials?
The Global Drug Manufacturing Supply Chain
One factor affecting the supply and cost of pharmaceutical drugs is the global drug manufacturing supply chain. A supply chain consists of the participants at each step in the process that takes a product from raw materials to finished goods sold to customers. As it relates to global drug manufacturing, the supply chain refers to the movement of the various components and materials essential to providing a drug for human consumption.
The pharmaceutical supply chain is a global, complex system. The key role players include raw material suppliers, drug manufacturers, regulatory agencies, wholesale distributors, pharmacies, pharmacy benefit managers (PBMs), health care providers, and clients (Kaylor, 2023). First, raw materials are sourced and transported for manufacturing. Pharmaceutical manufacturing in the United States has declined significantly, and up to 90 percent of needed raw materials are estimated to come from other countries (Constantino, 2021). Next, the drugs are transferred to wholesale distributors, who provide them to the pharmacies. Pharmacy benefit management companies are the intermediaries working with insurers, employers, and government programs to negotiate the prices the clients will pay for the prescriptions (Kaylor, 2023).
The supply chain’s quality and safety are essential to the United States’ national security and public health (Costantino, 2021). Standards related to the global drug manufacturing supply chain assist governments and drug manufacturers in increasing the availability of safe, quality medicines that are necessary to build client and health provider trust (U.S. Pharmacopeial Convention [USPC], 2023). Examples of standards include the processes employed by organizations, such as the FDA, before medications, foods, and other materials are deemed safe for human and animal consumption. These guidelines are necessary to promote a strong and resilient supply chain so that people have the drugs they need at the time they need them. It is imperative that such regulations are backed by science, producing high-quality development and manufacturing processes and high-quality drugs for human consumption (USPC, 2023).
The pharmaceutical supply chain faces several challenges, including supply chain visibility and rising prescription drug costs (Kaylor, 2023). These challenges became evident during the COVID-19 pandemic by negatively affecting the pharmaceutical supply chain in several ways (Choe et al., 2020):
- They prompted unexpected increases in demand for critical medications needed to treat clients with COVID-19.
- They disrupted critical medication production as supplies of these medications were rapidly depleted while manufacturers were unable to keep up with the demand.
- They delayed regulatory oversight of production as travel restrictions curtailed FDA officials’ ability to inspect manufacturing facilities.
- They interrupted global trade of medications as many countries limited their pharmaceutical exports to meet the increased demand in their own countries.
- They revealed a limited understanding of local and demand-driven shortages that are not always reflected in the current FDA database of drug shortages.
- They highlighted inadequacies in supply chain planning and management. The United States has limited ability to coordinate and share medications and instead must rely upon pharmaceutical wholesalers.
The recently established Supply Chain Disruption Task Force is working to address the supply chain issues by developing a series of recommendations for supply chain diversification (Edwards, 2021). In the interim, the United States is working to overhaul its strategic national stockpile program. The stockpile program was established to disperse medications around the country in the event of a short-term disaster or biological attack (Edwards, 2021). The United States is redesigning the program to incorporate a strategic stockpile of drug ingredients so that domestic manufacturers can quickly produce needed medications in the event of an emergency.
Pharmaceutical Costs
Americans spend more on prescription medications than citizens of other countries. A recent study determined that U.S. prescription drug prices were 2.56 times those in 32 comparable countries (Bosworth et al., 2022). Accordingly, pharmaceuticals are one of the fastest-growing components of health care spending in the United States (Ellis, 2019). In July 2022, the average price increase per drug was almost $250, an increase of 7.8 percent (Bosworth et al., 2022). That same year, the list prices of several drugs increased by more than $20,000 or 500 percent (Bosworth et al., 2022). Rising prescription drug costs are an issue for many Americans.
There are several reasons for the high drug costs (Rajkumar, 2020):
- Monopolies: Newer drugs do not yet have any alternatives or competition in the form of generic medications or comparable versions from other companies. Also, some established drugs are manufactured by a limited number of companies, decreasing competition.
- Disease severity: Clients with serious illnesses are usually willing to pay any price for a drug that can save or prolong their life.
- Research and development: Developing a new drug is a lengthy, costly process. It takes approximately 12 years and $3 billion dollars for a new drug to get approved; only 10 to 20 percent of drugs developed and tested make it to the market.
- Political power of the pharmaceutical industry: Although the federal government is aware of the need to address high drug prices, the pharmaceutical industry is an influential lobbyist that frequently limits the government’s attempts to enact change.
The increase in drug costs disproportionately impacts underrepresented and marginalized populations. As drug costs continue to rise, access to drugs will become even more problematic for these populations. Drug adherence may decline as individuals and families make difficult choices related to priorities such as choosing to pay for housing and food or for pharmaceuticals to treat disease (Ellis, 2019). This leads to continued health disparities.
State and national policymakers are exploring options to better control and lower drug costs. In 2022, Congress passed the Inflation Reduction Act to address high and rising drug prices (Bosworth et al., 2022). The law requires drug manufacturers to pay rebates to Medicare if the drug prices for Medicare beneficiaries exceed inflation.
Community health nurses must recognize the impact of high drug prices on their clients. When assessing a client’s medication history, nurses should determine if the client is adhering to the prescribed regime. If not, nurses should examine the client holistically to determine the cause. Clients may not take their medications as prescribed if they cannot afford them. Nurses should work with clients to identify programs that can help them pay for prescriptions. Alternatively, nurses could work with the prescribers to identify less costly alternatives for the client.
Read the scenario, and then respond to the questions that follow.
A client with a diagnosis of diabetes, hypertension, and congestive heart failure visits her local primary care physician for a six-week follow-up appointment after being discharged from the hospital with an exacerbation of her congestive heart failure. The client presents with shortness of breath, and her blood pressure is 190/100. The client did not bring her medications to her doctor’s visit as her discharge nurse instructed. She reports that she has been taking her medications as scheduled. The client is currently unemployed and has applied for Medicaid benefits.
- How should the nurse approach obtaining a more detailed medication history from the client?
- If the client indicates she is not taking her medications because she cannot afford them, what next step(s) should the nurse take?


2.6: Mineral Properties
Minerals are universal. A crystal of hematite on Mars will have the same properties as one on Earth, and the same as one on a planet orbiting another star. That’s good news for geology students who are planning interplanetary travel since we can use those properties to help us identify minerals anywhere. That doesn’t mean that it’s easy, however; identification of minerals takes a lot of practice. Some of the mineral properties that are useful for identification are as follows: color, streak, lustre, hardness, crystal habit, cleavage/fracture, density and a few others.
Colour
For most of us, color is one of our key ways of identifying objects. While some minerals have particularly distinctive colors that make good diagnostic properties, many do not, and for many, color is simply unreliable. The mineral sulfur (2.6.1 left) is always a distinctive and unique yellow. Hematite, on the other hand, is an example of a mineral for which color is not diagnostic. In some forms hematite is deep dull red, but in others it is black and shiny metallic (Figure \(\PageIndex{2}\)). Many other minerals can have a wide range of colors (e.g., quartz, feldspar, amphibole, fluorite, and calcite). In most cases, the variations in colors are a result of varying proportions of trace elements within the mineral. In the case of quartz, for example, yellow quartz (citrine) has trace amounts of ferric iron (Fe 3 + ), rose quartz has trace amounts of manganese, purple quartz (amethyst) has trace amounts of iron, and milky quartz, which is very common, has millions of fluid inclusions (tiny cavities, each filled with water).
Streak
In the context of minerals, “color” is what you see when light reflects off the surface of the sample. One reason that color can be so variable is that the type of surface is variable. It may be a crystal face or a fracture surface or a cleavage plane, and the crystals may be large or small depending on the nature of the rock. If we grind a small amount of the sample to a powder we get a much better indication of its actual color. This can easily be done by scraping a corner of the sample across a streak plate (a piece of unglazed porcelain) to make a streak . The result is that some of the mineral gets ground to a powder and we can get a better impression of its “true” color (Figure \(\PageIndex{2}\)).
Lustre
Lustre is the way light reflects off the surface of a mineral, and the degree to which it penetrates into the interior. The key distinction is between metallic and non-metallic lustres . Light does not pass through metals, and that is the main reason they look “metallic.” Even a thin sheet of metal—such as aluminum foil—will not allow light to pass through it. Many non-metallic minerals may look as if light will not pass through them, but if you take a closer look at a thin edge of the mineral you can see that it does. If a non-metallic mineral has a shiny, reflective surface, then it is called “glassy.” If it is dull and non-reflective, it is “earthy.” Other types of non-metallic lustres are “silky,” “pearly,” and “resinous.” Lustre is a good diagnostic property since most minerals will always appear either metallic or non-metallic. There are a few exceptions to this (e.g., hematite in Figure \(\PageIndex{1}\)).
Hardness
One of the most important diagnostic properties of a mineral is its hardness. In 1812 German mineralogist Friedrich Mohs came up with a list of 10 reasonably common minerals that had a wide range of hardnesses. These minerals are shown in Figure \(\PageIndex{3}\), with the Mohs scale of hardness along the bottom axis. In fact, while each mineral on the list is harder than the one before it, the relative measured hardnesses (vertical axis) are not linear. For example apatite is about three times harder than fluorite and diamond is three times harder than corundum.  These are tools that a geologist can use to measure the hardness of unknown minerals. For example, if you have a mineral that you can’t scratch with your fingernail, but you can scratch with a copper wire, then its hardness is between 2.5 and 3.5. And of course the minerals themselves can be used to test other minerals.
Crystal Habit
When minerals form within rocks, there is a possibility that they will form in distinctive crystal shapes if they formed slowly and if they are not crowded out by other pre-existing minerals. Every mineral has one or more distinctive crystal habits , but it is not that common, in ordinary rocks, for the shapes to be obvious. Quartz, for example, will form six-sided prisms with pointed ends (Figure \(\PageIndex{4}\)a), but this typically happens only when it crystallizes from a hot water solution within a cavity in an existing rock. Pyrite can form cubic crystals (Figure \(\PageIndex{4}\)b), but can also form crystals with 12 faces, known as dodecahedra (“dodeca” means 12). The mineral garnet also forms dodecahedral crystals (Figure \(\PageIndex{4}\)c).
Because well-formed crystals are rare in ordinary rocks, habit isn’t as useful a diagnostic feature as one might think. However, there are several minerals for which it is important. One is garnet, which is common in some metamorphic rocks and typically displays the dodecahedral shape. Another is amphibole, which forms long thin crystals, and is common in igneous rocks like granite (Figure \(\PageIndex{2}\)).
Mineral habit is often related to the regular arrangement of the molecules that make up the mineral. Some of the terms that are used to describe habit include bladed, botryoidal (grape-like), dendritic (branched), drusy (an encrustation of minerals), equant (similar in all dimensions), fibrous, platy, prismatic (long and thin), and stubby.
Cleavage and Fracture
Crystal habit is a reflection of how a mineral grows, while cleavage and fracture describe how it breaks. Cleavage and fracture are the most important diagnostic features of many minerals, and often the most difficult to understand and identify. Cleavage is what we see when a mineral breaks along a specific plane or planes, while fracture is an irregular break. Some minerals tend to cleave along planes at various fixed orientations, some do not cleave at all (they only fracture). Minerals that have cleavage can also fracture along surfaces that are not parallel to their cleavage planes.
As we’ve already discussed, the way that minerals break is determined by their atomic arrangement and specifically by the orientation of weaknesses within the lattice. Graphite and the micas, for example, have cleavage planes parallel to their sheets (Figures 2.2.5 and 2.4.5), and halite has three cleavage planes parallel to the lattice directions (Figure \(\PageIndex{6}\)).
Quartz has no cleavage because it has equally strong Si–O bonds in all directions, and feldspar has two cleavages at 90° to each other (Figure \(\PageIndex{5}\)).
One of the main difficulties with recognizing and describing cleavage is that it is visible only in individual crystals. Most rocks have small crystals and it’s very difficult to see the cleavage within those crystals. Geology students have to work hard to understand and recognize cleavage, but it’s worth the effort since it is a reliable diagnostic property for most minerals.
One last thing: it is important to recognize the difference between cleavage planes and crystal surfaces. As already noted, crystal surfaces are related to how a mineral grows while cleavage planes are related to how it breaks. In most minerals cleavage planes and crystal surfaces do not align with one-another. An exception is halite, which grows in cubic crystals and has cleavage along those same planes (Figure \(\PageIndex{1}\) and 2.2.6). But this doesn’t hold for most minerals. Quartz has crystal surfaces but no cleavage at all. Fluorite forms cubic crystals like those of halite, but it cleaves along planes that differ in orientation from the crystal surfaces. This is illustrated in Figure \(\PageIndex{6}\).
Density
Density is a measure of the mass of a mineral per unit volume, and it is a useful diagnostic tool in some cases. Most common minerals, such as quartz, feldspar, calcite, amphibole, and mica, have what we call “average density” (2.6 to 3.0 grams per cubic centimetre (g/cm 3 )), and it would be difficult to tell them apart on the basis of their density. On the other hand, many of the metallic minerals, such as pyrite, hematite, and magnetite, have densities over 5 g/cm 3 . They can easily be distinguished from the lighter minerals on the basis of density, but not necessarily from each other. A limitation of using density as a diagnostic tool is that one cannot assess it in minerals that are a small part of a rock that is mostly made up of other minerals.
Other Properties
Several other properties are also useful for identification of some minerals. For example, calcite is soluble in dilute acid and will give off bubbles of carbon dioxide. Magnetite is magnetic, so will affect a magnet. A few other minerals are weakly magnetic.
Image Descriptions
| Talc | Gypsum | Calcite | Fluorine | Apatite | Feldspar | Quartz | Topaz | Corundum | Diamond | |
|---|---|---|---|---|---|---|---|---|---|---|
| Measured Hardness | 50 | 60 | 105 | 200 | 659 | 700 | 1100 | 1648 | 2085 | 7000 |
| Mohs Hardness | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Media Attributions
- Figure \(\PageIndex{2}\): © Karla Panchuk. CC BY.
- Figure \(\PageIndex{4}\)a: Quartz Bresil © Didier Descouens. CC BY.
- Figure \(\PageIndex{4}\)b: Pyrite cubic crystals on marlstone © Carles Millan. CC BY-SA.
- Figure \(\PageIndex{4}\)c: Almandine garnet © Eurico Zimbres (FGEL/UERJ) and Tom Epaminondas (mineral collector). CC BY-SA.


4.4: Microbial Metabolism
Throughout earth’s history, microbial metabolism has been a driving force behind the development and maintenance of the planet’s biosphere. Eukaryotic organisms such as plants and animals typically depend on organic molecules for energy, growth, and reproduction. Prokaryotes, on the other hand, can metabolize a wide range of organic as well as inorganic matter, from complex organic molecules like cellulose to inorganic molecules and ions such as atmospheric nitrogen (N 2 ), molecular hydrogen (H 2 ), sulfide (S 2− ), manganese (II) ions (Mn 2+ ), ferrous iron (Fe 2+ ), and ferric iron (Fe 3+ ), to name a few. By metabolizing such substances, microbes chemically convert them to other forms. In some cases, microbial metabolism produces chemicals that can be harmful to other organisms; in others, it produces substances that are essential to the metabolism and survival of other life forms (Figure \(\PageIndex{1}\)).
-
- 4.4.1: Energy, Matter, and Enzymes
- Cellular processes such as the building or breaking down of complex molecules occur through series of stepwise, interconnected chemical reactions called metabolic pathways. The term anabolism refers to those endergonic metabolic pathways involved in biosynthesis, converting simple molecular building blocks into more complex molecules, and fueled by the use of cellular energy.
-
- 4.4.2: Catabolism of Carbohydrates
- Glycolysis is the first step in the breakdown of glucose, resulting in the formation of ATP, which is produced by substrate-level phosphorylation; NADH; and two pyruvate molecules. Glycolysis does not use oxygen and is not oxygen dependent. After glycolysis, a three-carbon pyruvate is decarboxylated to form a two-carbon acetyl group, coupled with the formation of NADH. The acetyl group is attached to a large carrier compound called coenzyme A.
-
- 4.4.3: Cellular Respiration
- Cellular respiration begins when electrons are transferred from NADH and FADH₂—through a series of chemical reactions to a final inorganic electron acceptor (either oxygen in aerobic respiration or non-oxygen inorganic molecules in anaerobic respiration). These electron transfers take place on the inner part of the cell membrane of prokaryotic cells or in specialized protein complexes in the inner membrane of the mitochondria of eukaryotic cells.
-
- 4.4.4: Fermentation
- Fermentation uses an organic molecule as a final electron acceptor to regenerate NAD⁺ from NADH so that glycolysis can continue. Fermentation does not involve an electron transport system, and no ATP is made by the fermentation process directly. Fermenters make very little ATP—only two ATP molecules per glucose molecule during glycolysis. Microbial fermentation processes have been used for the production of foods and pharmaceuticals, and for the identification of microbes.
-
- 4.4.5: Catabolism of Lipids and Proteins
- Collectively, microbes have the ability to degrade a wide variety of carbon sources besides carbohydrates, including lipids and proteins. The catabolic pathways for all of these molecules eventually connect into glycolysis and the Krebs cycle. Several types of lipids can be microbially degraded. Triglycerides are degraded by extracellular lipases, releasing fatty acids from the glycerol backbone. Phospholipids are degraded by phospholipases, releasing fatty acids and phosphorylated head groups.
-
- 4.4.6: Photosynthesis and the Importance of Light
- Heterotrophic organisms ranging from E. coli to humans rely on the chemical energy found mainly in carbohydrate molecules. Many of these carbohydrates are produced by photosynthesis, the biochemical process by which phototrophic organisms convert solar energy (sunlight) into chemical energy. Although photosynthesis is most commonly associated with plants, microbial photosynthesis is also a significant supplier of chemical energy, fueling many diverse ecosystems.
-
- 4.4.7: Biogeochemical Cycles
- Energy flows directionally through ecosystems, entering as sunlight for phototrophs or as inorganic molecules for chemoautotrophs. The six most common elements associated with organic molecules—carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur—take a variety of chemical forms and may exist for long periods in the atmosphere, on land, in water, or beneath earth’s surface.
Thumbnail: The Krebs cycle, also known as the citric acid cycle, is summarized here. Note incoming two-carbon acetyl results in the main outputs per turn of two CO 2 , three NADH, one FADH 2 , and one ATP (or GTP) molecules made by substrate-level phosphorylation. Two turns of the Krebs cycle are required to process all of the carbon from one glucose molecule. (CC BY 4.0; OpenStax )


5.3: Newton's First Law
- Describe Newton's first law of motion
- Recognize friction as an external force
- Define inertia
- Identify inertial reference frames
- Calculate equilibrium for a system
Experience suggests that an object at rest remains at rest if left alone and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. However, Newton’s first law gives a deeper explanation of this observation.
A body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force.
Note the repeated use of the verb “remains.” We can think of this law as preserving the status quo of motion. Also note the expression “constant velocity;” this means that the object maintains a path along a straight line, since neither the magnitude nor the direction of the velocity vector changes. We can use Figure \(\PageIndex{1}\) to consider the two parts of Newton’s first law.
Rather than contradicting our experience, Newton’s first law says that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force, which we defined earlier in the chapter. An object sliding across a table or floor slows down due to the net force of friction acting on the object. If friction disappears, will the object still slow down?
The idea of cause and effect is crucial in accurately describing what happens in various situations. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt. If we spray the surface with talcum powder to make the surface smoother, the object slides farther. If we make the surface even smoother by rubbing lubricating oil on it, the object slides farther yet. Extrapolating to a frictionless surface and ignoring air resistance, we can imagine the object sliding in a straight line indefinitely. Friction is thus the cause of slowing (consistent with Newton’s first law). The object would not slow down if friction were eliminated.
Consider an air hockey table (Figure \(\PageIndex{2}\)). When the air is turned off, the puck slides only a short distance before friction slows it to a stop. However, when the air is turned on, it creates a nearly frictionless surface, and the puck glides long distances without slowing down. Additionally, if we know enough about the friction, we can accurately predict how quickly the object slows down.
Newton’s first law is general and can be applied to anything from an object sliding on a table to a satellite in orbit to blood pumped from the heart. Experiments have verified that any change in velocity (speed or direction) must be caused by an external force. The idea of generally applicable or universal laws is important—it is a basic feature of all laws of physics. Identifying these laws is like recognizing patterns in nature from which further patterns can be discovered. The genius of Galileo, who first developed the idea for the first law of motion, and Newton, who clarified it, was to ask the fundamental question: “What is the cause?” Thinking in terms of cause and effect is fundamentally different from the typical ancient Greek approach, when questions such as “Why does a tiger have stripes?” would have been answered in Aristotelian fashion, such as “That is the nature of the beast.” The ability to think in terms of cause and effect is the ability to make a connection between an observed behavior and the surrounding world.
Gravitation and Inertia
Regardless of the scale of an object, whether a molecule or a subatomic particle, two properties remain valid and thus of interest to physics: gravitation and inertia. Both are connected to mass. Roughly speaking, mass is a measure of the amount of matter in something. Gravitation is the attraction of one mass to another, such as the attraction between yourself and Earth that holds your feet to the floor. The magnitude of this attraction is your weight, and it is a force.
Mass is also related to inertia , the ability of an object to resist changes in its motion—in other words, to resist acceleration. Newton’s first law is often called the law of inertia . As we know from experience, some objects have more inertia than others. It is more difficult to change the motion of a large boulder than that of a basketball, for example, because the boulder has more mass than the basketball. In other words, the inertia of an object is measured by its mass. The relationship between mass and weight is explored later in this chapter.
Inertial Reference Frames
Earlier, we stated Newton’s first law as “A body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force.” It can also be stated as “Every body remains in its state of uniform motion in a straight line unless it is compelled to change that state by forces acting on it.” To Newton, “uniform motion in a straight line” meant constant velocity, which includes the case of zero velocity, or rest. Therefore, the first law says that the velocity of an object remains constant if the net force on it is zero.
Newton’s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference frame: the inertial reference frame . In principle, we can make the net force on a body zero. If its velocity relative to a given frame is constant, then that frame is said to be inertial. So by definition, an inertial reference frame is a reference frame in which Newton’s first law is valid. Newton’s first law applies to objects with constant velocity. From this fact, we can infer the following statement.
A reference frame moving at constant velocity relative to an inertial frame is also inertial. A reference frame accelerating relative to an inertial frame is not inertial.
Are inertial frames common in nature? It turns out that well within experimental error, a reference frame at rest relative to the most distant, or “fixed,” stars is inertial. All frames moving uniformly with respect to this fixed-star frame are also inertial. For example, a nonrotating reference frame attached to the Sun is, for all practical purposes, inertial, because its velocity relative to the fixed stars does not vary by more than one part in 10 10 . Earth accelerates relative to the fixed stars because it rotates on its axis and revolves around the Sun; hence, a reference frame attached to its surface is not inertial. For most problems, however, such a frame serves as a sufficiently accurate approximation to an inertial frame, because the acceleration of a point on Earth’s surface relative to the fixed stars is rather small (< 3.4 x 10 −2 m/s 2 ). Thus, unless indicated otherwise, we consider reference frames fixed on Earth to be inertial.
Finally, no particular inertial frame is more special than any other. As far as the laws of nature are concerned, all inertial frames are equivalent. In analyzing a problem, we choose one inertial frame over another simply on the basis of convenience.
Newton’s First Law and Equilibrium
Newton’s first law tells us about the equilibrium of a system, which is the state in which the forces on the system are balanced. Returning to Forces and the ice skaters in Figure 5.2.2 , we know that the forces \(\vec{F}_{1}\) and \(\vec{F}_{2}\) combine to form a resultant force, or the net external force: \(\vec{F}_{R}\) = \(\vec{F}_{net}\) = \(\vec{F}_{1}\) + \(\vec{F}_{2}\). To create equilibrium, we require a balancing force that will produce a net force of zero. This force must be equal in magnitude but opposite in direction to \(\vec{F}_{R}\), which means the vector must be \(- \vec{F}_{R}\). Referring to the ice skaters, for which we found \(\vec{F}_{R}\) to be 30.0 \(\hat{i}\) + 40.0 \(\hat{j}\) N, we can determine the balancing force by simply finding \(- \vec{F}_{R}\) = −30.0 \(\hat{i}\) − 40.0 \(\hat{j}\) N. See the free-body diagram in Figure 5.2.2b .
We can give Newton’s first law in vector form:
\[\vec{v} = constant\; when\; \vec{F}_{net} = \vec{0}\; N \ldotp \label{5.2}\]
This equation says that a net force of zero implies that the velocity \(\vec{v}\) of the object is constant. (The word “constant” can indicate zero velocity.)
Newton’s first law is deceptively simple. If a car is at rest, the only forces acting on the car are weight and the contact force of the pavement pushing up on the car (Figure \(\PageIndex{3}\)). It is easy to understand that a nonzero net force is required to change the state of motion of the car. However, if the car is in motion with constant velocity, a common misconception is that the engine force propelling the car forward is larger in magnitude than the friction force that opposes forward motion. In fact, the two forces have identical magnitude.
Newton’s laws can be applied to all physical processes involving force and motion, including something as mundane as driving a car.
- Your car is parked outside your house. Does Newton’s first law apply in this situation? Why or why not?
- Your car moves at constant velocity down the street. Does Newton’s first law apply in this situation? Why or why not?
Strategy
In (a), we are considering the first part of Newton’s first law, dealing with a body at rest; in (b), we look at the second part of Newton’s first law for a body in motion.
Solution
- When your car is parked, all forces on the car must be balanced; the vector sum is 0 N. Thus, the net force is zero, and Newton’s first law applies. The acceleration of the car is zero, and in this case, the velocity is also zero.
- When your car is moving at constant velocity down the street, the net force must also be zero according to Newton’s first law. The car’s engine produces a forward force; friction, a force between the road and the tires of the car that opposes forward motion, has exactly the same magnitude as the engine force, producing the net force of zero. The body continues in its state of constant velocity until the net force becomes nonzero. Realize that a net force of zero means that an object is either at rest or moving with constant velocity, that is, it is not accelerating . What do you suppose happens when the car accelerates? We explore this idea in the next section.
Significance
As this example shows, there are two kinds of equilibrium. In (a), the car is at rest; we say it is in static equilibrium . In (b), the forces on the car are balanced, but the car is moving; we say that it is in dynamic equilibrium . (We examine this idea in more detail in Static Equilibrium and Elasticity .) Again, it is possible for two (or more) forces to act on an object yet for the object to move. In addition, a net force of zero cannot produce acceleration.
A skydiver opens his parachute, and shortly thereafter, he is moving at constant velocity. (a) What forces are acting on him? (b) Which force is bigger?
Engage in this simulation to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.


Skip to main content
3: Identity and Intercultural Communication
-
-
Last updated
-
-
Save as PDF
-
-
-
3.1: Foundations of Culture and Identity
-
The text discusses self-concept and identity formation, emphasizing the influence of various social agents like parents, peers, and media. Identities are categorized into personal, social, and cultural, and are fluid rather than static. The process of identity development varies across nondominant, dominant, and bi- or multiracial identities, with models highlighting stages like unexamined identity, resistance, and integration.
-
-
3.2: Exploring Specific Cultural Identities
-
The page explores how cultural identities like race, gender, sexual orientation, and ability are socially constructed rather than biologically determined. It delves into the historical context of these identities, discussing how they have evolved over time in response to social, political, and scientific influences. The text underscores the importance of communication in forming and expressing identities.
-
-
3.3: Identity and Migration
-
The adaptation process for individuals experiencing a new culture, known as acculturation, involves adjusting to different values, norms, and behaviors. Factors such as age, education, language proficiency, and cultural differences impact this adaptation, which can be either psychological or sociocultural. Acculturation can take forms like assimilation, integration, separation, and marginalization.


35.18: Religion as Comfort Versus Religion as Justification
I took out my Greek Testament… I opened accidentally in the epistle to the Hebrews, and the first words that offered to my view were these: [And be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee (Hebrews 13:5)]. I cannot but say they gave me great comfort, and thought myself, in that moment, equal to all the difficulties I foresaw and had to encounter with, through the divine protection: though I very well remembered the caution my pious and judicious uncle gave me. “Beware,” said he, “of the practice of some enthusiasts of our times, who
make the word of God literally an oracle, by opening it at particular times, and on particular occasions, presuming that where-ever they open, they are to apply the passage to themselves, or to the business they are about
; because many have thereby been led into spiritual pride, and others into despair, as they opened to a promise, or a curse; whilst others have but too often, in the same manner, pleaded a warrant from scripture to perpetuate wickedness, or to propagate error. Though,” added he, “
happy is the christian who by a prudent and rational use of the scriptures procures comfort to his soul
. For as the apostle says, Whatsoever things were written aforetime, were written for our learning, that we through patience, and comfort of the scriptures, might have hope.”
Winkfield, Unca Eliza. “Chapter V”.
The Female American,
edited by Michelle Burnham and James Freitas. Broadview, Ed. 2. p 68.
It’s easy to draw a connection (not a parallel) between Eliza’s words and Rowlandson’s
Narrative.
At every opportunity, Rowlandson sneaks away with the scripture, treating it as her guide, her oracle, and feeling as though she is beside the people quoted therein, or perhaps, who it was written specifically for. At the same time, we are shown a place in the text where Eliza could easily have done the same, but then remembers a speech her uncle gave her, relating it to us so that all are clear on the importance of avoiding exactly Rowlandson’s practice (a practice which gives Rowlandson, as Eliza’s uncle wonderfully puts it, a kind of misplaced “spiritual pride”). Telling Eliza of the importance of reading the text as a whole and not in pieces like bite-sized chunks of one-religion-prophesizes-all, he uses the phrase, “happy is the christian who by a prudent and rational use of the scriptures procures comfort to his soul” (Winkfield 68). This is where Eliza is able to regain her mental footing, so to speak, and uses the text as he tells her; a comfort to her soul. Examples of this are seen scattered throughout the text, where she quotes the scripture occasionally, but more often finds significance in her life around large parts of its narrative and values. This is a long way of saying that religion plays the role of her comforter and keeper throughout the text, guiding Eliza, as she allows, to being a stronger human, both mentally and emotionally, giving her the strength to continue even when she assumes she has none.
Religion is important in the text as it gives Eliza a guide to which she sets her moral compass. As her religion is viewed through the lens of her uncle’s experiences and sermons, she finds that it is easy to focus on the larger picture of the text as a whole, and is better able to use her knowledge for spiritual enrichment rather than justification for morally grey actions (as Rowlandson did in her text). Though it is not nearly as obviously prominent as in Rowlandson’s writing, Eliza’s mentions of her religion are not mere throwaway references to demonstrate her religious beliefs are still held, but rather, are references to her need to be in conversation with the scriptures she finds genuinely comforting.


6.5: Applications of Fourier Series
-
- Last updated
- Save as PDF
Periodically Forced Oscillation
Let us return to the forced oscillations. Consider a mass-spring system as before, where we have a mass \(m\) on a spring with spring constant \(k\), with damping \(c\), and a force \(F(t)\) applied to the mass. Suppose the forcing function \(F(t)\) is \(2L\)-periodic for some \(L>0\). We have already seen this problem in chapter 2 with a simple \(F(t)\).
The equation that governs this particular setup is
\[\label{eq:1} mx''(t)+cx'(t)+kx(t)=F(t). \]
The general solution consists of \(\eqref{eq:1}\) consists of the complementary solution \(x_c\), which solves the associated homogeneous equation \( mx''+cx'+kx=0\), and a particular solution of Equation \(\eqref{eq:1}\) we call \(x_p\). For \(c>0\), the complementary solution \(x_c\) will decay as time goes by. Therefore, we are mostly interested in a particular solution \(x_p\) that does not decay and is periodic with the same period as \(F(t)\). We call this particular solution the steady periodic solution and we write it as \(x_{sp}\) as before. What will be new in this section is that we consider an arbitrary forcing function \(F(t)\) instead of a simple cosine.
For simplicity, let us suppose that \(c=0\). The problem with \(c>0\) is very similar. The equation
\[ mx''+kx=0 \nonumber \]
has the general solution
\[ x(t)= A \cos(\omega_0 t)+ B \sin(\omega_0 t), \nonumber \]
where \( \omega_0= \sqrt{\dfrac{k}{m}}\). Any solution to \(mx''(t)+kx(t)=F(t)\) is of the form \(A \cos(\omega_0 t)+ B \sin(\omega_0 t)+x_{sp}\). The steady periodic solution \(x_{sp}\) has the same period as \(F(t)\).
In the spirit of the last section and the idea of undetermined coefficients we first write
\[ F(t)= \dfrac{c_0}{2}+ \sum^{\infty}_{n=1} c_n \cos \left(\dfrac{n \pi}{L}t \right)+ d_n \sin \left(\dfrac{n \pi}{L}t \right). \nonumber \]
Then we write a proposed steady periodic solution \(x\) as
\[ x(t)= \dfrac{a_0}{2}+ \sum^{\infty}_{n=1} a_n \cos \left(\dfrac{n \pi}{L}t \right)+ b_n \sin \left(\dfrac{n \pi}{L}t \right), \nonumber \]
where \(a_n\) and \(b_n\) are unknowns. We plug \(x\) into the differential equation and solve for \(a_n\) and \(b_n\) in terms of \(c_n\) and \(d_n\). This process is perhaps best understood by example.
Example \(\PageIndex{1}\)
Suppose that \( k=2\), and \( m=1\). The units are again the mks units (meters-kilograms-seconds). There is a jetpack strapped to the mass, which fires with a force of 1 newton for 1 second and then is off for 1 second, and so on. We want to find the steady periodic solution.
Solution
The equation is, therefore,
\[x''+2x=F(t), \nonumber \]
where \(F(t)\) is the step function
\[F(t)= \left\{ \begin{array}{ccc} 0 & {\rm{if}} & -1<t<0, \\ 1 & {\rm{if}} & 0<t<1, \end{array} \right. \nonumber \]
extended periodically. We write
\[ F(t)= \dfrac{c_0}{2}+ \sum^{\infty}_{n=1} c_n \cos(n \pi t)+ d_n \sin(n \pi t). \nonumber \]
We compute
\[\begin{align}\begin{aligned} c_n &= \int^1_{-1} F(t) \cos(n \pi t)dt= \int^1_{0} \cos(n \pi t)dt= 0 ~~~~~ {\rm{for}}~ n \geq 1, \\ c_0 &= \int^1_{-1} F(t) dt= \int^1_{0} dt=1, \\ d_n &= \int^1_{-1} F(t) \sin(n \pi t)dt \\ &= \int^1_{0} \sin(n \pi t)dt \\ &= \left[ \dfrac{- \cos(n \pi t)}{n \pi}\right]^1_{t=0} \\ &= \dfrac{1-(-1)^n}{\pi n}= \left\{ \begin{array}{ccc} \dfrac{2}{\pi n} & {\rm{if~}} n {\rm{~odd}}, \\ 0 & {\rm{if~}} n {\rm{~even}}. \end{array} \right.\end{aligned}\end{align} \nonumber \]
So
\[ F(t)= \dfrac{1}{2}+ \sum^{\infty}_{ \underset{n ~\rm{odd}}{n=1} }\dfrac{2}{\pi n} \sin(n \pi t). \nonumber \]
We want to try
\[ x(t)= \dfrac{a_0}{2}+ \sum_{n=1}^{\infty} a_n \cos(n \pi t)+ b_n \sin(n \pi t). \nonumber \]
Once we plug into the differential equation \( x'' + 2x = F(t)\), it is clear that \(a_n=0\) for \(n \geq 1\) as there are no corresponding terms in the series for \(F(t)\). Similarly \(b_n=0\) for \(n\) even. Hence we try
\[ x(t)= \dfrac{a_0}{2}+ \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} b_n \sin(n \pi t). \nonumber \]
We plug into the differential equation and obtain
\[\begin{align}\begin{aligned} x''+2x &= \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} \left[ -b_n n^2 \pi^2 \sin(n \pi t) \right] +a_0+2 \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} \left[ b_n \sin(n \pi t) \right] \\ &= a_0+ \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} b_n(2-n^2 \pi^2) \sin(n \pi t) \\ &= F(t)= \dfrac{1}{2}+ \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} \dfrac{2}{\pi n} \sin(n \pi t).\end{aligned}\end{align} \nonumber \]
So \(a_0= \dfrac{1}{2}\), \(b_n= 0\) for even \(n\), and for odd \(n\) we get
\[ b_n= \dfrac{2}{\pi n(2-n^2 \pi^2)}. \nonumber \]
The steady periodic solution has the Fourier series
\[ x_{sp}(t)= \dfrac{1}{4}+ \sum_{\underset{n ~\rm{odd}}{n=1}}^{\infty} \dfrac{2}{\pi n(2-n^2 \pi^2)} \sin(n \pi t). \nonumber \]
We know this is the steady periodic solution as it contains no terms of the complementary solution and it is periodic with the same period as \(F(t)\) itself. See Figure \(\PageIndex{1}\) for the plot of this solution.
Resonance
Just like when the forcing function was a simple cosine, resonance could still happen. Let us assume \(c=0\) and we will discuss only pure resonance. Again, take the equation
\[ mx''(t)+kx(t)=F(t). \nonumber \]
When we expand \(F(t)\) and find that some of its terms coincide with the complementary solution to \( mx''+kx=0\), we cannot use those terms in the guess. Just like before, they will disappear when we plug into the left hand side and we will get a contradictory equation (such as \(0=1\)). That is, suppose
\[ x_c=A \cos(\omega_0 t)+B \sin(\omega_0 t), \nonumber \]
where \( \omega_0= \dfrac{N \pi}{L}\) for some positive integer \(N\). In this case we have to modify our guess and try
\[ x(t)= \dfrac{a_0}{2}+t \left( a_N \cos \left( \dfrac{N \pi}{L}t \right)+ b_N \sin \left( \dfrac{N \pi}{L}t \right) \right) + \sum_{\underset{n \neq N}{n=1}}^{\infty} a_n \cos \left( \dfrac{n \pi}{L}t \right)+ b_n \sin \left( \dfrac{n \pi}{L}t \right). \nonumber \]
In other words, we multiply the offending term by \(t\). From then on, we proceed as before.
Of course, the solution will not be a Fourier series (it will not even be periodic) since it contains these terms multiplied by \(t\). Further, the terms \( t \left( a_N \cos \left( \dfrac{N \pi}{L}t \right)+ b_N \sin \left( \dfrac{N \pi}{L}t \right) \right) \) will eventually dominate and lead to wild oscillations. As before, this behavior is called pure resonance or just resonance .
Note that there now may be infinitely many resonance frequencies to hit. That is, as we change the frequency of \(F\) (we change \(L\)), different terms from the Fourier series of \(F\) may interfere with the complementary solution and will cause resonance. However, we should note that since everything is an approximation and in particular \(c\) is never actually zero but something very close to zero, only the first few resonance frequencies will matter.
Example \(\PageIndex{2}\)
Find the steady periodic solution to the equation
\[\label{eq:19} 2x''+18 \pi^2 x=F(t), \]
where
\[F(t)= \left\{ \begin{array}{ccc} -1 & {\rm{if}} & -1<t<0, \\ 1 & {\rm{if}} & 0<t<1, \end{array} \right. \nonumber \]
extended periodically. We note that
\[ F(t)= \sum^{\infty}_{ \underset{n ~\rm{odd}}{n=1} } \dfrac{4}{\pi n} \sin(n \pi t). \nonumber \]
Exercise \(\PageIndex{1}\)
Compute the Fourier series of \(F\) to verify the above equation.
As \(\sqrt{\frac{k}{m}}=\sqrt{\frac{18\pi ^{2}}{2}}=3\pi\), the solution to \(\eqref{eq:19}\) is
\[ x(t)= c_1 \cos(3 \pi t)+ c_2 \sin(3 \pi t)+x_p(t) \nonumber \]
for some particular solution \(x_p\).
If we just try an \(x_{p}\) given as a Fourier series with \(\sin (n\pi t)\) as usual, the complementary equation, \(2x''+18\pi^{2}x=0\), eats our \(3^{\text{rd}}\) harmonic. That is, the term with \(\sin (3\pi t)\) is already in in our complementary solution. Therefore, we pull that term out and multiply it by \(t\). We also add a cosine term to get everything right. That is, we try
\[ x_p(t)= a_3 t \cos(3 \pi t) + b_3 t \sin(3 \pi t) + \sum^{\infty}_{ \underset{\underset{n \neq 3}{n ~\rm{odd}}}{n=1} } b_n \sin(n \pi t). \nonumber \]
Let us compute the second derivative.
\[ x_p''(t)= -6a_3 \pi \sin(3 \pi t) -9 \pi^2 a_3 t \cos(3 \pi t) + 6b_3 \pi \cos(3 \pi t) -9 \pi^2 b_3 t \sin(3 \pi t) +\sum^{\infty}_{ \underset{\underset{n \neq 3}{n ~\rm{odd}}}{n=1} } (-n^2 \pi^2 b_n) \sin(n \pi t). \nonumber \]
We now plug into the left hand side of the differential equation.
\[\begin{align}\begin{aligned} 2x_p'' + 18\pi^2 x_p = & - 12 a_3 \pi \sin (3 \pi t) - 18\pi^2 a_3 t \cos (3 \pi t) + 12 b_3 \pi \cos (3 \pi t) - 18\pi^2 b_3 t \sin (3 \pi t) \\ & \phantom{\, - 12 a_3 \pi \sin (3 \pi t)} ~ {} + 18 \pi^2 a_3 t \cos (3 \pi t) \phantom{\, + 12 b_3 \pi \cos (3 \pi t)} ~ {} + 18 \pi^2 b_3 t \sin (3 \pi t) \\ & {} + \sum_{\substack{n=1 \\ n~\text{odd} \\ n\not= 3}}^\infty (-2n^2 \pi^2 b_n + 18\pi^2 b_n) \, \sin (n \pi t) . \end{aligned}\end{align} \nonumber \]
If we simplify we obtain
\[ 2x_p'' +18 \pi^2 x= -12a_3 \pi \sin(3 \pi t)+ 12b_3 \pi \cos(3 \pi t) +\sum^{\infty}_{ \underset{\underset{n \neq 3}{n ~\rm{odd}}}{n=1} } (-2n^2 \pi^2 b_n+ 18 \pi^2 b_n) \sin(n \pi t.) \nonumber \]
This series has to equal to the series for \(F(t)\). We equate the coefficients and solve for \(a_3\) and \(b_n\).
\[\begin{align}\begin{aligned} a_3 &= \frac{4/(3 \pi)}{-12 \pi}= \frac{-1}{9 \pi^2}, \\ b_3 &= 0, \\ b_n &= \frac{4}{n \pi(18 \pi^2 -2n^2 \pi^2)}=\frac{2}{\pi^3 n(9-n^2 )} ~~~~~~ {\rm{for~}} n {\rm{~odd~and~}} n \neq 3.\end{aligned}\end{align} \nonumber \]
That is,
\[ x_p(t)= \frac{-1}{9 \pi^2}t \cos(3 \pi t)+ \sum^{\infty}_{ \underset{\underset{n \neq 3}{n ~\rm{odd}}}{n=1} } \frac{2}{\pi^3 n(9-n^2)} \sin(n \pi t.) \nonumber \]
When \(c>0\), you will not have to worry about pure resonance. That is, there will never be any conflicts and you do not need to multiply any terms by \(t\). There is a corresponding concept of practical resonance and it is very similar to the ideas we already explored in Chapter 2 . Basically what happens in practical resonance is that one of the coefficients in the series for \(x_{sp}\) can get very big. We will not go into details here.
-
- Jiří Lebl ( Oklahoma State University ).These pages were supported by NSF grants DMS-0900885 and DMS-1362337.


1.6: Culture and Project Management
What Is Organizational Culture?
When working with internal and external customers on a project, it is essential to pay close attention to relationships, context, history, and the corporate culture. Corporate culture refers to the beliefs, attitudes, and values that the organization’s members share and the behaviours consistent with them (which they give rise to). Corporate culture sets one organization apart from another, and dictates how members of the organization will see you, interact with you, and sometimes judge you. Often, projects too have a specific culture, work norms, and social conventions.
Some aspects of corporate culture are easily observed; others are more difficult to discern. You can easily observe the office environment and how people dress and speak. In one company, individuals work separately in closed offices; in another, teams may work in a shared environment. The more subtle components of corporate culture, such as the values and overarching business philosophy, may not be readily apparent, but they are reflected in member behaviours, symbols, and conventions used.
Project Manager’s Checklist
Once the corporate culture has been identified, members should try to adapt to the frequency, formality, and type of communication customary in that culture. This adaptation will strongly affect project members’ productivity and satisfaction internally, as well as with the client organization.
- Which stakeholders will make the decision in this organization on this issue? Will your project decisions and documentation have to go up through several layers to get approval? If so, what are the criteria and values that may affect acceptance there? For example, is being on schedule the most important consideration? Cost? Quality?
- What type of communication among and between stakeholders is preferred? Do they want lengthy documents? Is “short and sweet” the typical standard?
- What medium of communication is preferred? What kind of medium is usually chosen for this type of situation? Check the files to see what others have done. Ask others in the organization.
- What vocabulary and format are used? What colours and designs are used (e.g., at Hewlett-Packard, all rectangles have curved corners)?
Project Team Challenges
Today’s globally distributed organizations (and projects) consist of people who have differing “worldviews.” Worldview is a looking glass through which people see the world as Bob Shebib describes: “[It is] a belief system about the nature of the universe, its perceived effect on human behaviour, and one’s place in the universe. Worldview is a fundamental core set of assumptions explaining cultural forces, the nature of humankind, the nature of good and evil, luck, fate, spirits, the power of significant others, the role of time, and the nature of our physical and natural resources” (Shebib, 2003, p. 296).
If, for example, a Canadian manager is sent to India to manage an R&D team or a joint venture, they are likely to have to “[cope] with eco-shock or the physiological, psychological, and social reaction to a new assignment ecology.” Hanging a shingle in a fluid and culturally diverse organization, project team, and work culture, a project manager may find new working relationships and hidden challenges have significant implications for performance and knowledge exchange – for the manager and colleagues at home and in the host country.
In most situations, there is simply no substitute for having a well-placed person from the host culture to guide the new person through the cultural nuances of getting things done. In fact, if this “intervention” isn’t present, it is likely to affect the person’s motivation or desire to continue trying to break through the cultural (and other) barriers. Indeed, optimal effectiveness in such situations requires learning of cultures in developing countries or international micro-cultures and sharing perceptions among the culturally diverse task participants on how to get things done. Project leaders require sensitivity and awareness of multicultural preferences. The following broad areas should be considered:
- Individual identity and role within the project versus family of origin and community
- Verbal and emotional expressiveness
- Relationship expectations
- Style of communication
- Language
- Personal priorities, values, and beliefs
- Time orientation
There are many interpersonal dynamics and intra-project challenges faced by a globally distributed team. Individual members and the team itself requires important social supports to mitigate uncertainty, conflict, motivational challenges, culture shock, and the more-encompassing eco-shock that comes from facing head-on the unfamiliar and diverse situations consistent with a different cultural and geographically distributed context.
Diverse and globally distributed project teams (i.e., different ethnic cultures, genders, ages, and functional capabilities), often working on complex projects spanning multiple time zones, geography, and history, and operating with tight deadlines in cost-conscious organizations, need to make time and resources available to physically meet each other, and connect (at the very least) at a formal “kick-off” meeting. Especially when working with team members from high-context cultures, it is essential to meet face-to-face, discover member’s individual identities and cultural preferences, share professional knowledge and personal stories, and observe critical verbal and non-verbal cues (that may not easily be observed online, or on the telephone). This is key to establishing a safer climate and building trust for stronger relationships among both team members and management.
Dealing with Conflict
The question isn’t whether, when, or with what frequency conflict will occur among intercultural team members — or what will create the conflict. If a team wants to overcome (or harness) conflict for effectiveness and productivity, the question is how to navigate and resolve the conflicts. Conflict that springs from diversity can actually assist the team in completing complex problem solving. However, if not navigated successfully, it can create relationship strain and derail achievement due to increased difficulties in communication and coordination.
As the global marketplace continues its rapid expansion, researchers are increasingly turning their attention to the issue of conflict management. Differing social and cultural values don’t necessarily increase the number of conflicts a team will experience, but they can have an impact on how conflicts are managed and resolved. Cultural awareness is needed for understanding and appreciating others’ values and behavioural norms. Without that, foreign assignments will become an overwhelming challenge. Self-awareness and skill development can aid in resolving the problematic conflict arising from cultural differences to help a team maintain good relations and remain productive.
References
Shebib, B. (2003). Choices: Interviewing and Counselling Skills for Canadians, 2nd edition, Pearson Education Canada Inc.
Text Attributions
This chapter of Project Management is a derivative of the following text:
- Project Management for Skills for All Careers by Project Management Open Resources and TAP-a-PM. © Creative Commons Attribution 3.0 Licence .