Week 3 - Solving second order ODEs

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

function(t,theta,b,g,l,m) write seperatly

then plot the figure after creating the plot then make a animation video usind for loop commend

take some initial and final coordinates then creat plot figure 2.

after creating the figure 2 then mention the string of pendulum and bob of pendulum and using the pause commend for ploting speed.

And finally using move commend for creat the amimation.

Errors facing,

mention wrong spelling for x label after correct that makes x axis named.

wrongly mention apostrophe for linewidth its shows error after removing that error resolved.

by mistake mentioned zero in maker , after it changed into o, make the animation video.

clear all
close all
clc
 b= 0.05;
 g= 9.81;
 l= 1;
 m= 1;
  
 % initial condition 
 theta_0 = [0;5];

 % time point
 t_span = linspace(0,10,500);

  % solve ODE
 [t,results] = ode45(@(t,theta) ode_function(t,theta,b,g,l,m),t_span,theta_0);
 
   plot(t,results(:,1))
 hold on
  plot(t,results(:,2))
  ylabel('plot')
xlabel('time')
 
% for loop for creat animation of pendulum

ct=1;
theta_1 = results(:,1);

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

    % initial coordinates
    x_start= 0;
    y_start= 0;
    theta_2 = theta_1(i);

    %final coordinates
    x_end = 1*sin(theta_2);
    y_end = -1*cos(theta_2);
    
    % plotting
    figure(2)
    %base of pendulum
 plot([-1,1],[0,0],'LineWidth',3,'Color','b')   
   hold on
   % string of pendulum
   line([x_start x_end],[y_start y_end],'linewidth',6,'color','r')
   hold on
   % bob of pendulum
   plot(x_end,y_end,'Marker','o','markersize',30,'MarkerFaceColor','g')
 axis([-2 2 -2 2])
   pause(0.03)
   hold off
   M(ct)= getframe(gcf);
   ct=ct+1;
    end

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


function [dtheta_dt] = ode_function(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
​

https://youtu.be/AB7XRszw8N0