Pendulum Wave Art Pattern using Python

import numpy as np

import matplotlib.pyplot as plt

import matplotlib.animation as animation

num_pendulums = 15

lengths = np.linspace(1, 2, num_pendulums)

g = 9.81  

time = np.linspace(0, 20, 1000)

periods = 2 * np.pi * np.sqrt(lengths / g)

angles = [np.cos(2 * np.pi * time / T) for T in periods]

x_pos = [l * np.sin(angle) for l, angle in zip(lengths, angles)]

y_pos = [-l * np.cos(angle) for l, angle in zip(lengths, angles)]

fig, ax = plt.subplots(figsize=(8, 8))

ax.set_xlim(-2.5, 2.5)

ax.set_ylim(-2.5, 0.5)

ax.set_aspect('equal')

ax.set_title('Pendulum Wave Art Plot')

lines = [ax.plot([], [], 'o-', markersize=10)[0] for _ in range(num_pendulums)]

def animate(i):

    for j, line in enumerate(lines):

        line.set_data([0, x_pos[j][i]], [0, y_pos[j][i]])

    return lines

ani = animation.FuncAnimation(fig, animate, frames=len(time), interval=30, blit=True)

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Importing Libraries

import numpy as np

import matplotlib.pyplot as plt

import matplotlib.animation as animation

NumPy: For efficient mathematical operations.

Matplotlib: For plotting and visualizing.

Matplotlib Animation: For creating the pendulum wave animation.

2. Initialization

num_pendulums = 15

lengths = np.linspace(1, 2, num_pendulums)

g = 9.81

time = np.linspace(0, 20, 1000)

num_pendulums: Number of pendulums in the animation (15 in this case).

lengths: Linearly spaced pendulum lengths from 1 to 2 meters using np.linspace.

g: Gravitational acceleration (9.81 m/s²).

time: Array representing 1000 time steps from 0 to 20 seconds.

3. Calculating Pendulum Motion

periods = 2 * np.pi * np.sqrt(lengths / g)

Formula Used: The period of a simple pendulum is given by:

T=2π root l/g

T = Period of oscillation

L = Length of the pendulum

g = Gravitational acceleration

4. Calculating Angular Position (θ)

angles = [np.cos(2 * np.pi * time / T) for T in periods]

Using the equation:

θ(t)=cos(2πt/T)

The angles are calculated for each pendulum over time using cosine function for oscillatory motion.

5. Converting to Cartesian Coordinates

x_pos = [l * np.sin(angle) for l, angle in zip(lengths, angles)]

y_pos = [-l * np.cos(angle) for l, angle in zip(lengths, angles)]

The x and y positions of the pendulum are calculated using trigonometry:

x=Lsin(θ)

y=−Lcos(θ)

The negative y ensures the pendulum moves downwards.

6. Plot Setup

fig, ax = plt.subplots(figsize=(8, 8))

ax.set_xlim(-2.5, 2.5)

ax.set_ylim(-2.5, 0.5)

ax.set_aspect('equal')

ax.set_title('Pendulum Wave Art Plot')

A figure of size 8x8 is created.

x and y limits are adjusted to fit all pendulums.

ax.set_aspect('equal') ensures equal scaling on both axes.

A title is added.

7. Creating the Pendulums

lines = [ax.plot([], [], 'o-', markersize=10)[0] for _ in range(num_pendulums)]

The pendulums are visualized using markers ('o-') with a size of 10.

Each pendulum is represented as a line starting from the origin (0, 0).

8. Animation Function

def animate(i):

    for j, line in enumerate(lines):

        line.set_data([0, x_pos[j][i]], [0, y_pos[j][i]])

    return lines

animate() updates the pendulum positions for each frame (i).

set_data() updates the line data to simulate the swinging motion.

9. Creating and Displaying Animation

ani = animation.FuncAnimation(fig, animate, frames=len(time), interval=30, blit=True)

plt.show()

FuncAnimation: Handles the animation by repeatedly calling the animate() function.

interval=30 means each frame is displayed for 30 milliseconds.

blit=True optimizes the rendering for smoother animations.