import numpy as np
import matplotlib.pyplot as plt

time = 60
dt = 0.001
m = 0.1
g = 9.81
theta = 5*np.pi/6
k = 200
L0 = 1
r = np.zeros((n,2),float)
v = np.zeros((n,2),float)
a = np.zeros((n,2),float)
t = np.zeros((n,1),float)
n = int(np.ceil(time/dt))
r0 = np.array([L0*np.sin(theta) ,L0*np.cos(theta) ])
v0 = np.array([1.0, 0.0])
r[0,:] = r0
v[0,:] = v0


for i in range(n):
    a[i,:] = (-m*g*np.array[0,1]-k*(((r[i,0])**2+(r[i,1])**2)-L0))/m*(r[i,0]        /((r[i,0])**2+(r[i,1])**2))

    v[i+1,:] = v[i,:] + a[i,:]*dt
    r[i+1,:] = r[i,:] + v[i+1,:]*dt

plt.plot(r[1:i, 0], r[1:i, 1])
plt.show()