Week 3 - Solving second order ODEs

Theory-In Engineering,ODE is used to describe the transient behaviour of a system.a simple example is a pendulum

The way pendulum moves depends on the newtons second law.when this law is written down ,we get a second order ordinary differential equation that describes the position of the ball with respect to time.

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)/1)
	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,l,g,m))

plt.plot(t,disvelo[:,0],'-',label='displacement')
plt.plot(t,disvelo[:,1],'--',label='velocity')
plt.legend()
plt.xlabel('time')
plt.ylabel('displacementvelocity')
plt.show()

y=disvelo[:,0]
ct=1
for ang in y :
	x1=0;y1=0
	x2=1*math.sin(ang)
	y2=1*math.cos(ang)
	file='test%05d.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.xlime([-1.5,1.5])
	plt.ylime([-1.5,1.5])
	plt.savefig(file)
	ct=ct+1