Week 3 - Solving second order ODEs

Matlab program that solves the following ODE. This ODE represents the equation of motion of a simple pendulum with damping.

`(d^2theta)/dt^2+b/m (d theta)/dt+g/Lsin theta=0`

here

g=gravity=9.81 meter/sec^2

`b=damping cofficient=0.05`

m=mass =1 Kg

L=length=1 meter

Matlab code that solves this equation and create the animation of simple pendulam motion

clear all
close all
clc

%inputs
b=0.05;
g=9.81;
l=1;
m=1;

%initial conditions
%at t=0 angular displacement=0 and angular velocity=3
theta_0=[0;3];

%Time points
t=linspace(0,20,150);

%solve ODE
[t,result]=ode45(@(t,theta)ode_func(t,theta,b,g,l,m),t,theta_0)
%plotting of the angular displacement and angular velocity
plot(t,result(:,1))
hold on
plot(t,result(:,2))      
%labelling

xlabel('time')
ylabel('plot')
legend('angular displacement','angular velocity')
%Animation of pendulam motion
%counter value
ct=1;
%initial point of rod
 x0=0;
 y0=0;
for i=1:length(t)
   
    x=l*sin(result(i,1));
    y=-l*cos(result(i,1));
    figure(2)
    plot([-1 1],[0 0],'linewidth',6,'color','g')
  
    line([x0,x],[y0,y],'linewidth',3,'color','b')
     hold on
    plot(x,y,'o','markersize',15,'markerfacecolor','r')
    
    axis([-1.5,1.5,-1.5,1.5]);
    hold off
    M(ct)=getframe(gcf);  %create a frame of all the plotes
     ct=ct+1;
end
     %creation of movie
movie(M)
videofile=VideoWriter('pendulam_avi','uncompressed AVI')
open(videofile)
writeVideo(videofile,M)
close(videofile)

Outputs

the plot of the angular diplacement and velocity with respect of time is given

the link of the created animation is given below

https://drive.google.com/file/d/1TaR1DcO5GZ9zTINIPLAsv4jsXbZCLFcX/view?usp=sharing