Week 4.1 - Solving second order ODEs

https://youtu.be/-rNmcEZOlU0

%pendulam

%input



g=9.81;
l=1;
m=1;
b=0.05;

theta=[0;3];                  (angular displacement=0 & angular velocity =3 rad/s)

t_span=linspace(0,20,200);    (time span from 0-20 sec)

%Solving differential equation

[t,results]=ode45(@(t,theta)ode_eqn(g,l,m,b,t,theta),t_span,theta) (operator for 
                                                        ordinary differential equation )




%plotting                     (for loop is used to assign each value of x to X1 and Y1)

x=results(:,1);               (array has been made by choosing the first column from the 
                               results array)
ct=1;
for i=1:length(x)

    X0=0;
    Y0=0;


Y1=-l*cosd(x(i))              (negative value is used so that the pendulam direction can 
                               be reversed)

X1=l*sind(x(i))

%plotting the reference line 

plot([-1 1] , [0 0 ],'color','r','LineWidth',3 ) ( A line is plotted passing through the 
                                                   fixed point where the pendulam moves)

hold on

%plotting the positions of pendulam 

plot([X0 X1],[Y0 Y1],'color','b','linewidth',2) (various points of pendulam is plotted 
                                                 with different values of time)
                                            

%plotting the curve

plot( X1,Y1,'marker','o','MarkerSize',30,'Color','k','MarkerFaceColor','k')   (path 
                                                      traced by the pendulam is plotted)


axis([-2 2 -2 2])

pause(0.03)

hold off                 (hold off restricts the marking of all points )

M(ct)=getframe(gcf);     (operator for making frames of different positions of pendulam)


 ct=ct+1;                (for incrementing the number of frames)

end

% Animation

movie(M)

 videofile=VideoWriter('pendulam.avi,matlab video')

 open(videofile)               (file is opened )

 writeVideo(videofile,M)       (video is written in the opened file)

 close(videofile)               (video file is closed)



error in coding: The value X1 and Y1 where interchanged hence the pendulam ball was in upward positions

steps taken to overcome error :All the code where executed step by step and the value of X1 and Y1 are interchanged from the error condition.