simplependuumgraphssss.ipynb

Kernel: Python 3 (system-wide)

#Import recquired models
import numpy as np
import matplotlib.pyplot as plt

#This allows us to code for ODEs
from scipy.integrate import odeint

#Setting values
g = 9.81
L = 2

#Function- We convert the SHM ODE of a pendulum into 2 first order ODEs
def model(y,t,g,L):
    
    #theta'(t) = omega(t)
    #omega'(t) = -(g/L)*(sin(theta(t)))
    
    theta, omega = y
    dydt = [omega, -(g/L)*(np.sin(theta))]
    return dydt
    

#initial conditions
#sets that at time=0, angular velocity is 3 radians per second
y0 = [0-0.1,0.0]

#time points
t = np.linspace(0,10,101)

#solve ODE
sol = odeint(model, y0, t, args=(g,L))

#plotting results
plt.plot(t, sol[:, 0], 'b')
plt.ylabel('Angular displacement (rad)')
plt.xlabel('Time (seconds)')
plt.title('Fig 4')
plt.grid()
plt.show()
plt.show()

#Import recquired models
import numpy as np
import matplotlib.pyplot as plt

#This allows us to code for ODEs
from scipy.integrate import odeint

#Setting values
g = 9.81
L = 2

#Function- We convert the SHM ODE of a pendulum into 2 first order ODEs
def model(y,t,g,L):
    
    #theta'(t) = omega(t)
    #omega'(t) = -(g/L)*(sin(theta(t)))
    
    theta, omega = y
    dydt = [omega, -(g/L)*(np.sin(theta))]
    return dydt
    

#initial conditions
#sets that at time=0, angular velocity is 3 radians per second
y0 = [0-0.1,0.0]

#time points
t = np.linspace(0,10,101)

#solve ODE
sol = odeint(model, y0, t, args=(g,L))

#plotting results
plt.plot(t, sol[:, 1], 'b')
plt.ylabel('Angular velocity (rad per seconds)')
plt.xlabel('Time (seconds)')
plt.title('Fig 5')
plt.grid()
plt.show()
plt.show()

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

M=12
m=1
g=9.81

def Atwood(y,t,M,m,g):
    theta, omega, radius, Rho = y
    dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))]
    return dydt

y0 = [(1.1*np.pi)/2 ,0 ,1 ,0]
t = np.linspace(0,100,10000000)
sul = odeint(Atwood, y0, t, args=(M,m,g))

A=12
a=1
g=9.81

def second(y,t,A,a,g):
    theta, omega, radius, Rho = y
    dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(A+a))*(a*radius*(omega**2)-A*g+a*g*(np.cos(theta)))]
    return dydt

y1 = [(np.pi)/2 ,0 ,1 ,0]
t = np.linspace(0,100,10000000)
sal = odeint(second, y1, t, args=(A,a,g))


plt.plot(sal[:,0], sal[:,1], 'r')
plt.plot(sul[:,0], sul[:,1], 'g')
plt.ylabel('Angular velocity')
plt.xlabel('Angular displacement')
plt.title('Fig 12 - Phase Plot')
plt.grid()
plt.show()