import matplotlib.pyplot as plt
import numpy as np

##############################
# non-ideal pendulum

plt.clf()

n = 10000
dt = 0.001


theta=[]
omega=[]

theta.append(3.)
omega.append(0.)

for i in range(1,n):
   theta.append(theta[i-1] + omega[i-1]*dt)
   omega.append(omega[i-1] - np.sin(theta[i-1])*dt)

plt.plot(theta)

# second run

theta2=[]
omega=[]

theta2.append(1.)
omega.append(0.)

for i in range(1,n):
   theta2.append(theta2[i-1] + omega[i-1]*dt)
   omega.append(omega[i-1] - np.sin(theta2[i-1])*dt)


plt.plot(theta2)

plt.show()