Week 4.1 - Solving second order ODEs

creating function name ode_func :-

%defining function for ODE 
function [dtheta_dt] = ode_func(t,theta,b,g,l,m)
         
         % defining theta1 & theta2
         theta1 = theta(1);
         theta2 = theta(2);
         %1st ODE 
         dtheta1_dt=theta2;
         %2nd ODE
         dtheta2_dt=-(b/m)*theta2-(g/l)*sin(theta1);
         %combining theta & theta2
         dtheta_dt=[dtheta1_dt;dtheta2_dt];

end

Main Code :-

clear all
close all
clc

% Input variables for simple pendulum
b=0.05; %damping coefficient.
g=9.81;  % acceleration due to gravity m/s^2
l=1;     % length of pendulum in m
m=1;   %mass of the ball in kg,

%initial condition fo displacement and velocity
theta_0=[0;3];

%time points arrey
t_span = linspace(0,20,500);

%solve ODE
%ODE45 is the inbuilt command, t & theta is the main input of ode45 comand
%it is the function of t & theta
%ode_func is the function created having input of t,theta,b,g,l,m.
% & t_span is the time arrey & theta_0 is the initial condition
[t,results]=ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);

%plot between the time and results, results is the column vwctor having two
%column 1st is displacement and 2nd is velociti
plot(t,results(:,1)) % plot between time and displacement

hold on
plot(t,results(:,2)) % plot between time and velocity
xlabel('time')
ylabel('plot')

figure(2)
ct=1;

% craeting a loop for changing position of the pendulum throug different
% dispalcement over length of t_span
for i=1:length(results(:,1))
    x0=0;
    y0=0;
   

    x1=l*sin(results(i,1));
    y1=-l*cos(results(i,1)); % neagtive sign indiacate that the y1 is alwase negative as it is in the 3rd & 4th quadrant
    
    % ploting the horizontal line
    plot([-1.5 1.5],[0 0],'linewidth',2)
    hold on
    
    %ploting the length of of pendulum
    plot([x0 x1],[y0 y1],'linewidth',3,'color','b')

    %ploting the sphear of size 20
    plot(x1,y1,'o','markersize',20,'Color','r')
        % giving axis limits
        axis([-1.5 1.5 -1.5 1.5])
        %giving a pause between changing position
        pause(0.001)
        % for creating a movie using command frame 
        M(ct) = getframe(gcf);
        hold off
        % incremenat counter
        ct=ct+1;


end

%create a movie file    
movie(M)
videofile = VideoWriter('simple_pendulum.avi')
%opening a video file
open(videofile)
%writing a video into file
writeVideo(videofile,M)
%close video
close(videofile)

Output is attached as video file please find