simple pendulum with image processing code
import numpy as np
from scipy.integrate import odeint
import math
import matplotlib.pyplot as plt
"""
damping: effects that reduce the amplitude of the vibrations
"""
def ode_func(theta,t,b,g,l,m):
theta1=theta[0]
theta2=theta[1]
#first ode
dtheta1_dt=theta2
#second ode
dtheta2_dt=-((b/m)*(theta2))-((g/l)*math.sin(theta1));
dtheta_dt=[dtheta1_dt,dtheta2_dt]
return dtheta_dt
b=0.05 # damping coeffient(material property that indicate the material to bounce back)
# material with high damping coefficient used as the shock absorbers
g=9.81 # acceleration due to the gravity
l=1 #length of the string
m=1 #mass of the bob
#intial conditions
theta_0=[0,3]
# time plot
t=np.linspace(0,20,200)
#T = len(t)
# solvimg the ode
theta = odeint(ode_func,theta_0,t,args=(b,g,l,m))
plt.figure(1)
plt.plot(t,theta[:,0],'b--',label=r'$\frac{d\theta_1}{dt}=\theta2$')
plt.plot(t,theta[:,1],'r--',label=r'$\frac{d\theta_2}{dt}=-\frac{b}{m}\theta_2-\frac{g}{L}sin\theta_1$')
plt.xlabel('time(s)')
plt.ylabel('plot')
plt.legend(loc='best')
plt.show()
ite = 1
# Create a loop for the animation
for t in theta[:,0]:
x0=0
y0=0
x1=(l*math.sin(t))
y1 = -(l*math.cos(t))
filename = str(ite)+'.png'
ite=ite+1
#plotting
plt.figure()
plt.plot([-0.5,0.5],[0,0],'black',linewidth=5) # plotting the base line of the pendulum
plt.plot([x0,x1],[y0,y1],linewidth=3,color='r')
plt.plot(x0,y0,'o',markersize=5) # highlighting the point
plt.plot(x1,y1,'o',markersize=30,color='blue') # highlighting the point
plt.xlim([-1.5,1.5]) #defining the x limit.
plt.ylim([-1.5,1.5]) # defining the y limit.
plt.title('Animation of of Simple Pendulum')
plt.savefig(filename)