Week 3 - Solving second order ODEs

Aim:

The aim is to solve the simple pendullum, with the following criteria,

L=1 metre,

m=1 kg,

b=0.05.

g=9.81 m/s2.

Simulate the motion between 0-20 sec, for angular displacement=0,angular velocity=3 rad/sec at time t=0.

Procedure:

In this L = length,

m = mass in kg,

b = damping coefficient,

g = gravity,

import math

import numpy as n1

import matplotlib.pyplot as plt 

from scipy.integrate import odeint

def model(initial,t,b,l,g,m):

	t1 = initial[0]

	t2 = initial[1]

	dt1=t2

	dt2=(-b* t2/m)-(g * math.sin(t1)/l)

	dt=[dt1,dt2]

	return dt

b = 0.05

l = 1

g = 9.81

m = 1

initial=[0,3]

t = n1.linspace(0, 20, 200)

disvelo=odeint(model, initial,t,args=(b,1,g,m))

plt.plot(t,disvelo [:,0],'-', label='displacement')

plt.plot(t,disvelo[:,1], '--', label='velocity')

plt.legend()

plt.xlabel('time')

plt.ylabel('displacement velocity')

plt.show()

y=disvelo [:,0]

ct = 1

for ang in y:

	x1 = 0; y1 = 0

	x2=l * math.sin(ang)

	y2=l * math.cos(ang)

	file='test\%o5d.png'%ct

	plt.figure()

	plt.plot ([-1.5, 1.5], [0,0], linewidth = 8)

	plt.plot([x1,x2], [y1,y2], linewidth=3)

	plt.plot(x2,y2, 'o',markersize=15)

	plt.xlim([-1.5,1.5])

	plt.ylim([-1.5,1.5])

	plt.savefig(file)

	ct = ct + 1

Result :

The code has been completed successfully and the result has been added, the video has been uploaded in the assest.