Question

Plotting trajectories Classical Mechanics (Python)

Question: In the plot, set v = 1 m/s, ω = 1 1/s, and plot the trajectory for t ∈ [−6π, 6π].

Code:

import numpy as np
import matplotlib.pyplot as plt

tx=[]
for i in range(180):
    tx.append(i)

radianConverter = np.pi/180
x_2 = [1*t*np.cos(2*np.pi*t*radianConverter) for t in tx]
y_2 = [1*t*np.sin(2*np.pi*t*radianConverter) for t in tx]
plt.figure(figsize=[10,10])
plt.grid(True)
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.plot(x_2,y_2)
plt.show()

What changes do I have to do in order to fit the question parameters?

Answer 1

I have made the required changes as per the question parameters:
1. Since t ∈ [−6π, 6π] so I executed the loop from i = -6*180 to 6*180
2. ω = 1 1/s, so radianConverter is adjusted, radianConverter = 11* np.pi/180

//MODIFIED PROGRAM IS BELOW

import numpy as np
import matplotlib.pyplot as plt

tx=[]
i = -6*180;
for i in range(6*180):
tx.append(i)

radianConverter = 11* np.pi/180
x_2 = [1*t*np.cos(2*np.pi*t*radianConverter) for t in tx]
y_2 = [1*t*np.sin(2*np.pi*t*radianConverter) for t in tx]
plt.figure(figsize=[10,10])
plt.grid(True)
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.plot(x_2,y_2)
plt.show()

The resultant output figure after modification is: