Transient behaviour of a simple pendulum

%step 1 
%Clearing previous workspace & sessions
clear all 
close all
clc
 
%Step 2
%Inputs
b=0.05;
g=9.81;
l=1;
m=1;

%Step 3
%GIving Initial Conditions
theta_ic =[0;3];

%Step4
%Defining time interval with linspace command
t_span = linspace(0,10,500);

%Step 5
%Solve ODE & Calling the fucntion ode_func
[t,results] = ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_ic);

%Step 6
figure(1)
hold on
plot(t,results(:,1),'color','r','linewidth',2)
plot(t,results(:,2),'color','b','linewidth',2)
legend('Angular displacement','Angular Velocity')
hold off
xlabel('Time')
ylabel('Plot')

%Step 7
displacement = results(:,1);
velocity = results(:,2);
ct =1;
%Step 8

for i=1:length(displacement)
    
    %Step 9
    X0 =0;
    Y0=0;
    X1 = 1*cos(displacement(i)-pi/2);
    Y1 = 1*sin(displacement(i)-pi/2);
    
    %Step 10
    plot([-1 1],[0.75 0.75],'linewidth',17,'color','b')
    hold on
    
    %Step 11
    plot([X0 X1],[Y0 Y1],'linewidth',3,'color','b');
    
    %Step 12
    plot(X1,Y1,'-o','markersize',30','markerfacecolor','r','markeredgecolor','black');
     plot(X0,Y0,'-o','markersize',5','markerfacecolor','black');
     axis([-1.5 1.5 -1.5 1]);
     
     %Step 13
     displ =displacement(i);
     velo = velocity(i);
      txt1=['Angular displacement:',num2str(displ),'rad'];
      text(-0.5 ,0.75,txt1,'color','r');
      txt2 =['Angular Velocity:',num2str(velo),'rad/s'];
      text(-0.5,0.5,txt2,'color','b'); 
      pause(0.002)
     
      
      %Step 14
      P(ct) = getframe(gcf);
      ct=ct+1;
       hold off
      
end
%Step 15

movie(P);
videofile =VideoWriter('pendulum.avi','uncompressed AVI');
open(videofile);
writeVideo(videofile,P);
close(videofile);




%Function for ODE


function [dtheta_dt] = ode_func(t,theta,b,g,l,m)

    theta1=theta(1)
    theta2=theta(2)

    dtheta1_dt =theta2;
    dtheta2_dt =-(b/m)*theta2-(g/l)*sin(theta1);
    dtheta_dt = [dtheta1_dt;dtheta2_dt];

end

Stepwise Explanation:

1. Clearing previous workspaces and closing all plots.
2. Defining given inputs.
3. Giving initial conditions of angular displacement and velocity
4. Defining interval with linspace command
5. Calling the ode_func and solving the ODE
6. Graph plotting which show variation of angular displacement and velocity.
7. Defining array for angular displacement & velocity.
8. Constructing the ‘for‘ loop to depict different position of the pendulum.
9. Calculating the starting and ending position of the pendulum
10. Creating the support for the pendulum
11. Drawing the pendulum rop using co-ordinates.
12. Creating the pendulum ball using the markersize & markerfacecolor command
13. Writing the corresponding value of angular displacement and velocity.
14. Defining the labels for the animation
15. Commands for creating the animation
16. Creating the ode45 function for the calculation of angular displacement and velocity.