fourier_pluck_string.py

import numpy as np
import matplotlib.pyplot as plt

h = 1
p = np.pi*1/3
m = np.arange(1,101)
A_m = 2*h*np.sin(m*p)/(m**2*p*(np.pi-p))
x = np.linspace(0,np.pi,150)
# f = A_m* np.sin(m[np.newaxis,:]*x[:,np.newaxis])
f = A_m * np.sin(np.outer(x,m))
f=f.T
# plt.plot(x, f[:, 0], label='First column', alpha=0.7)
# plt.plot(x, f[:, 1], label='Second column', alpha=0.7)
plt.plot(x, f[:2, :].sum(1), label='Sum of first 2 columns', alpha=0.7)
plt.plot(x, f[:5, :].sum(1), label='Sum of first 5 columns', alpha=0.7)
plt.plot(x, f[:9, :].sum(1), label='Sum of first 9 columns', alpha=0.7)
plt.plot(x, f.sum(1), label='Sum of all columns', alpha=0.7)
plt.legend()
plt.show()

t = np.linspace(0,2*np.pi,200)
tmp = np.cos(np.outer(t,m))
f_full = f[np.newaxis,:,:]*tmp[:,:,np.newaxis]

X, T = np.meshgrid(x, t)
Z = f_full.sum(1)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, T, Z, cmap='viridis')  # Use a colormap for better visualization

ax.set_xlabel('X-axis')
ax.set_ylabel('T-axis')
ax.set_zlabel('Z-axis (f_full sum)')
ax.set_title('3D Surface Plot of f_full')
plt.show()