import matplotlib.pyplot as plt
import numpy as np

# fj?rkonstanten
k = 2 # kg/s^2
# massen
m = 10 # kg

# vinkelfrekvensen
omega_0 = np.sqrt( k/m )

# amplitudene
a_1 = 0.78
a_2 = 0.5

# fasene
phi_1 = 0.
phi_2 = 0.

# tidsskrit
dt = 0.1
# antall punkter
nt = 1000
# tidslinie
ts = np.arange(nt)*dt

# posisjonene
x1 = + a_1*np.cos( omega_0*ts - phi_1 ) \
     + a_2*np.cos( np.sqrt(3)*omega_0*ts - phi_2 )
x2 = + a_1*np.cos( omega_0*ts - phi_1 ) \
     - a_2*np.cos( np.sqrt(3)*omega_0*ts - phi_2)
# hastighetene
v1 = - a_1*omega_0*np.sin( omega_0*ts - phi_1 ) \
     - a_2*omega_0*np.sin( np.sqrt(3)*omega_0*ts - phi_2 )
v2 = - a_1*omega_0*np.sin( omega_0*ts - phi_1 ) \
     + a_2*omega_0*np.sin( np.sqrt(3)*omega_0*ts - phi_2 )

# plot posisjonene
plt.figure()
plt.plot(ts,x1,ts,x2)

# plot i faserom
plt.figure()
plt.plot(x1,v1)
plt.axis('equal')