Week 3 - Solving second order ODEs

REPORT ON TRASIENT BEHAVIOR OF SIMPLE PANDULUM

Created by Shahbaaz khan Deoda

On 17 may 2020

AIM: - To simulate the transient behavior of pendulum.

GOVERNING EQUATION: -

Simple harmonic motion is followed by pendulum oscillation of second order.

OBJECTIVE: - To draw the animation and code the program.

PROGRAM BODY: -

import numpy as np 
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import math

# function that return the the value of thata array
def model(theta,t,b,g,l,m):
	theta1 = theta[0]
	theta2 = theta[1]
	dtheta1_dt = theta2
	dtheta2_dt = -(b/m)*theta2-(g/l)*math.sin(theta1)
	dtheta_dt = [dtheta1_dt, dtheta2_dt]
	return dtheta_dt


b = 0.05
g = 9.81
l = 1
m = 0.1

#initial condition
theta_0 = [0,3]

#time array
t = np.linspace(0,20,300)

#solve ode
theta = odeint(model,theta_0,t,args = (b,g,l,m))
"""
#plot results
plt.plot(t,theta[:,0],'b-',label=r'displacement')
plt.plot(t,theta[:,1],'r--',label=r'velocity')
plt.ylabel('plot')
plt.xlabel('time')
plt.legend()
plt.show()"""


#animation
x0 = 0
y0 = 0
ct = 1

for i in range(0,300):
	s = theta[i,0]
	x1 = l*math.sin(s)
	y1 = -l*math.cos(s)
	filename = str(ct) + '.png'
	ct = ct + 1  
	# plot
	plt.figure()
	plt.plot([x0,x1],[y0,y1],color='b',lw=3)
	plt.plot([-0.6,0.6],[y0,y0],color='g',lw=3)
	plt.plot([x1],[y1],'o',markersize=20,color='r')
	plt.xlim([-1.2,1])
	plt.ylim([-1.2,0.2])
	plt.savefig(filename)
plt.show()
	

CONCLUSION: - we have successfully coded the program.