Week 3 - Solving second order ODEs

AIM

TO determine the oridenary differntial equation and to create the pendulam animation

FORMULA USED

ODE_FUNCTION EXPLANATION

BODY OF THE CONTENT

1. we start with clear all close all and clc command
2. and finding the intial condition theta_0 = [0;3]
3. and t_span = linspace of 0 to 500 into 20 values
4. then solve the ode [t,results] by using ode_function(t,theta,b,g,l,m)
5. we make a plot using plot command (t,results)

clear all
close all
clc

b=0.05;
g=9.81;
l=1;
m=0.1;
t = 0
% 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);

plot(t,results(:,1))
hold on
plot(t,results(:,2))
ylabel('plot')
xlabel('time')

ct = 1
theta = results(:,1)
for i = 1:length(theta)
    x1 = 0
    y1 = 2
    x2 = -1*sin(theta(i))
    y2 = -1*cos(theta(i))
    figure(2)
    plot([-1.5,1.5],[2,2])
    hold on
    plot([x1,x2],[y1,y2])
    plot(x2,y2,'o',MarkerSize = 30,MarkerFaceColor='black',MarkerEdgeColor='black')
    hold off
    xlim([-2.5,2.5])
    ylim([-2.5,2.5])
    M(ct) = getframe(gcf);
    ct = ct+1;
end

%creating animation
movie(M)
vediofile = VideoWriter('pendulum animation','Uncompressed AVI');
open(vediofile)
writeVideo(vediofile,M)
close(vediofile)