Week 4.1 - Solving second order ODEs

Solving second order ODEs

1) Step wise explanation of code.

* Inputs

*Angular velocity

*Entering displacement and velocity

*Solving through ODE 45 function - with function in other file

*Entering 'for' loop

*Creating Animation

https://drive.google.com/file/d/1G72VM7mpDWQyo3rNydzLKrj3CLWlF2cC/view?usp=sharing

Errors :-

Unable to determine scalar and numeric value. Raised Mentoring session to overcome problem.

Screenshot of error.

% program for 2 ODE function.
clear all
close all
clc
%inputs
b=0.05;
m=1;
l=1;
g=9.81;


% angular velocity
theta_0 = [0;3];

% motion
t_span=linspace(0,20,500);

%solve ODE
% ode45 is an inbuilt function, ode_func is elaborating ode45.
[t, result] = ode45(@(t,theta) bode_func(t,theta,b,g,l,m) ,t_span,theta_0);
plot(t, result(:,1))
hold on
plot(t,result(:,2))
amplitude=result(:,1)

%x=[0:5];
ct=1;
for i=1:length(amplitude) %1:length(t_span)
    angle=amplitude(i);
    title('simple pendulum')
    x0=0;
    y0=0;
    x1=l*sin(angle);
    y1=-l*cos(angle);
    figure(2)
    plot([x0 x1], [y0 y1],'linewidth',3,'color', 'red');
    hold on
    plot(x1,y1,'o','MarkerSize',20,'MarkerFaceColor',[1 1 0]);
    hold on
    plot([-1.1 1.1],[0  0],'linewidth',3,'color', 'blue');
    axis([-1.5 1.5 -1.5 0.5]);
    hold off
    grid on;
    pause(0.001)
    %plot([x0 x1], [y0 y1],'linewidth',3,'color', 'red')
    M(ct)=getframe(gcf);
    ct=ct+1;
end
movie(M);
videofile=VideoWriter('Aode.avi','Uncompressed AVI');
open(videofile);
writeVideo(videofile,M);
close(videofile)

function [dtheta_dt]=bode_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