# Symbolic Calculations


```python
import sympy as sm
sm.init_printing()
import numpy as np
import scipy as sp
import scipy.integrate
import matplotlib as mpl
mpl.rcParams['mathtext.fontset']='stix'
import matplotlib.pyplot as plt
import sympy.physics.units as u
u.miles.convert_to(u.km).n()
```

Differential equation for the Damped Harmonic Oscillator:
$$
\large
\frac{d^{2}x(t)}{dt^{2}}+2\gamma\omega_{0}\frac{dx(t)}{dt}+\omega_{0}^{2}x(t) = 0
$$


```python
t,omega0 = sm.symbols('t,omega_0', positive=True)
gamma = sm.symbols('gamma',complex=True)
x = sm.Function('x')
ode = 2*gamma*omega0*x(t).diff(t)+omega0**2*x(t)+x(t).diff(t,2)
ode
```


```python
sm.dsolve(ode)
```


```python

```

96e7cf64b94acf0b807422b6a6b65f67ffeb9171
ipynb
Jupyter Notebook
python/Vectors/Untitled.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/Untitled.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/Untitled.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
Qwen/Qwen-72B
1. YES
2. YES