# Program for the motion of a particle subject to an external
# force f(x) = -x.   We have divided the total time 2*pi into
# 10000 intervals with an equal time step.   The position and
# velocity of the particle are written out at every 500 steps.

import numpy as np

N = 10001    # number of time points
IN = 500     # interval between outputs
PI=3.14159265358979
DT   = 2.0*PI/(N-1)

X = np.arange(N, dtype=float)        # position
T = np.arange(N, dtype=float)        # time 
V = np.arange(N, dtype=float)        # velocity

# Assign constants, initial position, and initial velocity

X[0] = 0.0
T[0] = 0.0
V[0] = 1.0

# Recursion for position and velocity at later time

I = 0
while I < N-1:
    T[I+1] = DT*(I+1)
    X[I+1] = X[I]+V[I]*DT
    V[I+1] = V[I]-X[I]*DT
    I += 1
    
# Write the position and velocity every 500 steps

I = 0
while I < N:
    print(str(T[I]) + "  " + str(X[I]) + "  " + str(V[I])) 
    I += 500