import numpy as np
import matplotlib.pyplot as plt

n = 1000000
t = np.logspace(np.log10(10), np.log10(500), n)

# parameters
A = [1, 1, 1.5, 1.5]
d = [.004, .001, .002, .0015]
f = [3, 1, 2, 2.5]

x = A[0]*np.sin(t*f[0])*np.exp(-d[0]*t) + A[1]*np.sin(t*f[1])*np.exp(-d[1]*t)
y = A[2]*np.sin(t*f[2])*np.exp(-d[2]*t) + A[3]*np.sin(t*f[3])*np.exp(-d[3]*t)

plt.plot(x, y, 'k', linewidth=.1)
plt.axis('off')
plt.show()

plt.plot(np.sin(t*f[0])*np.exp(-d[0]*t), linewidth=.5)
#plt.plot(np.sin(t*f[0]), linewidth=.5)
#plt.plot(np.sin(t*f[0])*np.exp(-d[0]*5*t), linewidth=.5)
plt.show()