Week 3 - Solving second order ODEs

Youtube link: https://youtu.be/5_eSd3UHuB4

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

function called for the program

clear all 
close all
clc
b=0.05;
g=9.81;
l=1;
m=0.1;

%initial condition 
theta_0=[0;3];

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

% solve ode 
[t, results]=ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);
figure(1)
plot (t,results(:,1))
hold on 
plot (t,results(:,2))
ylabel("Plot")
xlabel('Time(sec)')
title('2nd order Derivative ')
% For loop for movie

ct=1;
for i =1:length(results(:,1))
x0=0
y0=0
x1= l*sin(results(i,1));
y1= -l*cos(results (i,1));

% plotting the animation
figure (2)
plot([-1 1], [0 0], 'linewidth', 5)
hold on
plot([x0 x1], [y0 y1], 'linewidth',3)
hold on
plot(x1,y1, 'o', 'markersize',20, 'markerFacecolor', 'c')
title('A Pendulum 2nd order Derivative ')
axis ([-1.5 1.5 -1.5 1])
pause (0.0000002)
hold off
M(ct)= getframe(gcf);
ct=ct+1;
    end

movie(M)
videofile = VideoWriter('Pendulum.avi','Uncompressed AVI')
open(videofile)
writeVideo(videofile,M)
close(videofile)

Program to be executed..

Graph plotted for pendulum motion,

Movie ploted

clear command,initial command,and then formula to solve with calling the function.

Code for ploting the graph.

For loop for the movie as the needed despc. and the specs for the movie and calling for the frames and saving it nd then execute it...

error found in line 10 : this was used instead of ; then the error was solved

there we conclude ODE is used to describe the transient behavior of a system.