% Program to solve the ode and simulate the motion of a pendulum.

% Declaring constants and initialising the values.

b=0.005;

g=9.81;

l=1;

m=1;

% Defining the parameters

theta_0 = [0;5];

t_span = linspace(0,10,500);

% Function calling statement.

[t,results] = ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);

% Plotting the curve

figure(1)

plot(t,results(:,1))

hold on

plot(t,results(:,2))

xlabel('Time')

ylabel('Theta and Velocity')

%Simulation of the pendulum

ct =1;

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

    x0=0;

    y0=0;

    x1 = l* sin(results(i,1));

    y1 = -l* cos(results(i,1));

    figure(2)

    plot([-1 1],[0 0],'linewidth',4,'color','k')

    axis([-2 2 -2 2]);

    hold on

    line([x0 x1],[y0 y1],'linewidth',2,'color','b')

    hold on

    plot(x1,y1,'.','markersize',30,'color','r')

    grid on

    hold off

    M(ct) = getframe(gcf);

    ct = ct+1;

end

% Creating animation

movie(M)

videofile = VideoWriter('Pendulum_Movement.avi','Uncompressed AVI');

open(videofile)

writeVideo(videofile,M)

close(videofile)

%ODE function

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