Week 3 - Solving second order ODEs

https://drive.google.com/file/d/1a05FPlpUgImqmy6KCX4KolQE3LeEFtv-/view?usp=sharing

%given inputs

%damping coefficient
b=0.05;

%mass(kg)
m=1;

%length (m)
l=1;

%gravity(m/s^2)
g=9.81;

%initial condition
%angular displacement=0 and angular velocity =3 m/s
theta_0=[0;3];

%time span
%pendulum oscillates 0-20 secs
%linspace - 1st value represents starting point of angle
%2nd point refers ending point of angle and last point refers no of values
t_span=linspace(0,20,300);

%solving ODE
%here ode45 was used its a function that solves ordinary,partial differential equations
%here it is 4th order runge kutta method...
%calling the function ode_func
[t,results]=ode45(@(t,theta) ode_func(t,theta,b,m,g,l),t_span,theta_0);

%plotting angular displacement and angular velocity with respect to time
figure(1)
plot(t,results(:,1))

%hold on used to add new plot in existing plot
hold on

plot(t,results(:,2))

%title is used for title of plot
title('motion')
%legend is used to create labels for each plot
legend('angular dispalacement','angular velocity')

%xlabel is used to define x axis
xlabel('time')

%ylabel is used to define y axis (i:e) displacement and velocity
ylabel('plot')

%counter was defined before starting for loop
%at every position of the ball ct stores the data
ct=1;

%for loop allows code to executed repeatedly the start and end points have
%been defined 

for i=1:length(results(:,1))

    %x0 and y0 is fixed point
    x0=0;
    y0=0;
    
    % x1 and y1 will be position of ball
    x1=1*sin(results(i,1));
    y1=-1*cos(results(i,1));

    %plotting pendulum for motion 
    figure(2)
    %plot for fixed line
    plot([-1 1],[0 0])
    hold on
    
    %pendulum string as line in blue color
    plot([x0 x1],[y0 y1],'linewidth',5,'Color','b')
    hold on
    
    %bob fixed to string with size 40 and red color
    plot(x1, y1,'o','markersize',40,'Color','r')
    
    %axis limits respect to x,y axis
    axis([-1.5 1.5 -1.5 1])

    %pause command gives better visualization of the plot
    pause(0.03)
    
    hold off
    %ALL total frames resulting are stored in  array M
    %getframe captures the individual frame in gcf
    M(ct)=getframe(gcf)

    %ctrepresents every frame the counter(ct) is incremented by  1(ct+1)
    ct=ct+1
end

%making the video file
%movie is used to create video of frames generated to variable M
movie(M)

%videowriter is used to assign the format of the video
%here avi format is used
videofile=VideoWriter('simple_pendulum.avi','uncompressed AVI');

%open command is used to open the video
open(videofile)

%write video is used to write the video with plot frames 
writeVideo(videofile,M)

%close command is used to close the video file
close(videofile)

%function program will be called in  main program to solve ode
%here 0=01 and d01/dt=02 in given equation 
function [dtheta_dt] = ode_func(t,theta,b,m,g,l)

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