# Eulers metode for harmonisk oscillator

import numpy as np
import matplotlib.pyplot as plt


x0 = 2
v0 = 0
dt = 0.05
tMax = 50

# a,v,x er akselerasjon, fart, posisjon 

n = int(tMax/dt)
t = np.zeros(n)
a = np.zeros(n)
v = np.zeros(n)
x = np.zeros(n)

x[0] = x0
v[0] = v0

for i in range(n-1):
    t[i+1] = (i+1)*dt
    a[i] = -x[i]
    v[i+1] = v[i] + a[i]*dt
    x[i+1] = x[i] + v[i]*dt

plt.plot(t,x,linewidth=2, label='Eulers metode')
plt.plot(t,x0*np.cos(t),linewidth=2, label='Analytisk l?sning')
plt.legend(loc='upper left')
plt.xlabel('t')
plt.ylabel('x(t)')
plt.savefig('HOEuler.pdf')
plt.show()