Week 3 - Solving second order ODEs

clc
clear all
close all

%Input Parameters
b = 0.05;
g = 9.81;
l = 1;
m = 1;

%Initial Conditions
alpha0 = [0;3];
time_span = linspace(0,20,500);

%Function Call Statement
[t,results] = ode45(@(t,alpha) pendulum_func(t,alpha,b,g,l,m),time_span, alpha0);

%Plot
plot(t,results(:,1))
hold on
plot(t,results(:,2))
xlabel('Time')
ylabel('Plot')
grid on



figure(2)

%counter for frame
ct = 1;
for i = 1:length(time_span)
    x0 = 0;
    y0 = 0;
    x1 = l*sin(results(i,1));
    y1 = -l*cos(results(i,1));
    plot([-0.6 0.6],[0 0],'linewidth',12)
    hold on
    plot([x0 x1],[y0 y1],'color','b','linewidth',3)
    axis([-3 1 -3 1])
    hold on
    plot(x1,y1,'o','MarkerSize',35,'MarkerFaceColor','g')
    hold off
    axis([-1 1 -1.5 1])
    pause(0.001)
    M(ct) = getframe(gcf);
    ct = ct+1;
    grid on
end

%Animation
movie(M)
videofile = VideoWriter('ode_2nd_order.avi','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

FUNCTION PROGRAM

function [dalpha_dt] = pendulum_func(t,alpha,b,g,l,m)
    alpha1 = alpha(1);
    alpha2 = alpha(2);
    dalpha1_dt = alpha2;
    dalpha2_dt = -(b/m)*alpha2-(g/l)*sin(alpha1);
    dalpha_dt = [dalpha1_dt; dalpha2_dt];
end

OUTPUTS

PROJECT PUBLISH LINK

https://skill-lync.com/projects/ode-and-pendulum-animation

YOUTUBE LINK

https://www.youtube.com/watch?v=fMQgbA0c4Zg