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 # Q 2A


#d2x/dt2 + gamma*dx/dt + k*x = 0

#take gamma = 0.4, k = 1 and solve using suitable scipy function


import numpy as np

from scipy.integrate import odeint

import matplotlib.pyplot as plt


gam = 0.4

k =  1.


def damp(x, t):

    return [x[1], -k*x[0]-gam*x[1]]


x0 = [1.0, 0.0]


t = np.linspace(0,20,1001)


sol = odeint(damp, x0, t)


plt.plot(t, sol[:,0], 'r', label="x")

plt.xlabel("time(t)")

plt.ylabel("x")

plt.axhline()

plt.title("Damped Harmonic Oscillator")

plt.legend()

plt.show()


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