Question

python code: Create a phase plot of a damped driven pendulum using odeint. Show a graph of angle as a function of time and angular velocity as a function of angle. Show each step in the code.

Answer 1

Python Code :

import numpy as np
from scipy.integrate import odeint
import math
import matplotlib.pyplot as plt
#finding the differentiation
def differentiation(variables,time,a,b,c,d):
   x = variables[0]
   y = variables[1]
   dx = y
   dt = -(a/d)*y-c*math.sin(x)
   dx_dt =[dx,dt]
   return dx_dt
#input data
a=0.05
b=9.81
c=1
d=1
#initial condition
initial = [0,3]
#plot the time
time = np.linspace(0,20,240)

data = odeint(differentiation,initial,time,args = (a,b,c,d))
#creating the
name=1
for i in range(0,240):
   name_of_file = str(name)+'.png'
   name= name+1
   plt.figure()
   plt.plot([10,c*math.sin(data[i,0])+10],[10,10-c*math.cos(data[i,
   0])],marker="o")
   plt.xlim([0,20])
   plt.ylim([0,20])
   plt.savefig(name_of_file)
plt.plot(time,data[:,0],'b-')
plt.plot(time,data[:,1],'r--')
plt.show()

You will 240 images as output.Few are given below.FInal output will be in final image ie.., 240.png

output 1 :

output 2 :

output 3 :

Output 4 :

Output5 :

Final ouput :