simple pendulum motion using matlab

% Main Program

 

clear all;
close all;
clc
% Week 2 Solving 2nd order ODE using MATLAB

g = 9.81; % Acceleration of gravity
l = 1;    % Length of Pendalum
m = 0.1;  % Masss of Pendalum
r=0.1;    % Radius of Pendalum  

% Initial Conditions
theta_0 = [0;5];

% Time Points
t_span = linspace(0,2,100);

% Compute Natural Frequency
omega=g/(l*m);

% Solve ODE
[t, results] = ode45(@(t,theta) f_ode(t,theta,omega),t_span,theta_0);

% Plot Responses
figure(1)
plot(t,results(:,1))
hold on
plot(t,results(:,2))
ylabel(\'Responses\')
xlabel(\'Time\')
legend(\'Displacement\',\'Velocity\');


%animation
ct=1;
for i = 1:length(t_span);
    THETA = results(i,1);
    
    %Coordinates for pendulum
    x1 = l*sin(THETA);
    y1 = -l*cos(THETA);
    
    % Plot 
    figure(2)
   
    plot([0 x1],[0 y1],\'linewidth\',5)
    
    axis([ -2*l 2*l -2*l 2*l]);
    title(\'Single Pendulum (Harmonic Motion)\')

    M(ct)=getframe(gcf);
    ct=ct+1;
end

% Create Animation
movie(M)
videofile=VideoWriter(\'PENDULUM.avi\',\'Uncompressed AVI\');
open(videofile)
writeVideo(videofile,M)
close(videofile)

function [dtheta_dt]=f_ode(t,theta,omega)

theta1=theta(1);
theta2=theta(2);
dtheta1_dt=theta2;
dtheta2_dt= -omega^2*sind(theta1);
dtheta_dt=[dtheta1_dt;dtheta2_dt];
end

video link

https://youtu.be/XIq8xrzSpxE