import numpy as np
import matplotlib.pyplot as plt
from math import sqrt
#Variable Definitions
N = 500
dur = 2.0
dr = dur/float(N-1)
#creating the array
y = np.zeros([N,2])
y[0,0] = 15
y[0,1] = 0#runge kutta algorithm
def rk4(y, r, dr, deriv):
k1 = dr * deriv(y,r)
k2 = dr *...