Week 3 - Solving second order ODEs

Main program

%Solving second order ODE
close all
clear all
clc

%Inputs
b= 0.05; %Damping co-efficient; 
g= 9.81; %Gravity (m/s^2);
l= 1; %Length (m);
m= 1; %Mass (kg);

%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')
legend('Angular displacement', 'Angular velocity')
title('Angular displacement vs Angular velocity')

ct=1;

theta2=results(:,1);

for i=1:length(theta2)
    theta=theta2(i);
    x0=0;
    y0=0;
    x1= l*sin(theta);
    y1= -l*cos(theta);
        
        %Plot
        figure(2)
        plot([-1 1],[0 0],"color","k","linewidth",3)
        hold on
        plot([x0 x1],[y0 y1],'color','m')
        plot(x1,y1,'o','markers',10,'markerfacecolor','b')
        hold off;        
        grid on;
        title('Pendulum displacement')
        axis([-1 1 -1.5 0.5])
        pause(0.01)
        hold off
        

        M(ct)= getframe(gcf);
        ct=ct+1;
    
end

movie(M)
videofile = VideoWriter('Pendulum_displacement','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

Function

%Function code for ode
function [dtheta_dt] = ode_func(t, theta, b, g, l, m)
theta1=theta(1);
theta2=theta(2);
dtheta1_dt= theta2;
dtheta2_dt= -(b/l)*theta2-(g/l)*sin(theta1);
dtheta_dt = [dtheta1_dt; dtheta2_dt]
end

Report

Step-wise explanation of your code.

1. Basic inputs like close all clear all clc.
2. Giving inputs or known data.
3. Giving a function name and defining the function or formula.
4. Plotting the graphs accordingly with desired labels.

Mention the errors faced while programming.

1. Incorrect dimensions of matrix.
2. Missed element wise operator and paranthesis.
3. Typographical errors.
4. Plotting of pendulum displacement in graph was difficult.

Steps taken to overcome those errors.

1. By providing the element wise operator.
2. Correct use of paranthesis and brackets.
3. Practising to avoid typographical errors.
4. Took help of Sai from skill-lync to get correct understanding of ODE function and inputs.

Youtube video link for Pendulum displacement video

https://youtu.be/hyuYh3tz2fY