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Solution Review: Harmonographs

Understand how to simulate and visualize harmonographs by coding pendulum motions with varied parameters. Learn to generate unique patterns, superimpose multiple pendulums, and create colorful, sliced plots. This lesson reinforces practical Python skills needed for scientific applications in motion simulation and plotting.

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Solution 1 #

C++
import numpy as np
import matplotlib.pyplot as plt
# defining function with default paramters value
def pendulum(t, A=1, f=100, p=0, d=0.05):
  return (A * np.sin (2 * np.pi * f * t + p) * np.exp(-1 * d * t))
# creating array for time
t = np.linspace(0, 2 * np.pi, 1000)
x_t = pendulum(t, 1, 2, 0, 0.5)
# plotting and setting labels
plt.figure(figsize=(12, 9), dpi=200)
plt.plot(t, x_t)
# setting labels
plt.title('Damped Pendulum')
plt.xlabel('t')
plt.ylabel('x(t)')
# saving figure
plt.savefig('output/harmonograph1.png')

Explanation #

  • In lines 5 - 6, we have defined the function pendulum() and set the default values for A, f, p, and d.

  • In line 9, we have created an array for time t.

  • In line 10, we have used custom arguments for the pendulum() function to generate data for a pendulum moving along the x-axis.

  • In lines 13 - 14, we are plotting the motion of the pendulum x_t against time t.

Solution 2

We have to plot the following equations:

x(t)=2sin(8πt−1)e−0.05t+sin(4πt−π2)e−0.01tx(t)=2sin(8\pi t -1)e^{-0.05t}+sin(4\pi t -\frac{\pi}{2})e^{-0.01t} ...