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  1. Home/
  2. Syed Saquib/
  3. Week 3 - Solving second order ODEs

Week 3 - Solving second order ODEs

Aim-To solve second order ordinary differential equation using matlab Objectives- To solve the second order ODE with graph of velocity v/s displacement Data- L= 1 meter t=0 M=1 kg b=0.05 g=9.81 m/s^2   Program- 1. code function of ODE45 for main program-   function[dtheta_dt]=ode_func(t,theta,b,g,l,m)…

    • Syed Saquib

      updated on 23 Apr 2022

    Aim-To solve second order ordinary differential equation using matlab

    Objectives- To solve the second order ODE with graph of velocity v/s displacement

    Data- L= 1 meter

    t=0

    M=1 kg

    b=0.05

    g=9.81 m/s^2

     

    Program-

    1. code function of ODE45 for main program-

     

    function[dtheta_dt]=ode_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
     
     
     
     
     
    2. Main program-
     
     
    clear all
    close all
    clc
    b=0.05;
    g=9.81;
    l=1;
    m=0.1
    %initial condition
    theta_0=[0;5];
    %time points
    t_span=linspace(0,20,500);
    % to 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('time')
    xlabel('velocity')
    legend('Displacement','Anglular velocity')
    grid on
    hold off
    displacement=results(:,1);
    velocity=results(:,2);
    %fixed coordinates
    x0=0;
    y0=0;
    ct=1;
    for i = 1:length(displacement)
    %coordinates
    x1=1*sin(displacement(i));
    y1=-1*cos(displacement(i));
    figure(2)
    %plotfixed link
    plot([-2 2],[0 0],'linewidth',15,'color','b')
    hold on
    plot([x0 x1],[y0 y1],'linewidth',4)
    plot(x1,y1,'-o','markersize',20,'markerfacecolor','b')
    %axisetting
    axis([-2 2 -2 2])
    % to chnage the frame movie
    M(ct)=getframe(gcf);
    ct=ct+1;
    hold off
    end
    movie(M)
    videofile=VideoWriter('simple pendulum.avi','Uncompressed AVI');
    open(videofile)
    writeVideo(videofile,M)
    close(videofile)
     
     
    Results-
     
     
    Postion of the setup-
     
     
     
    Animation-
     
    https://youtu.be/Rmw6D85LJlg
     
     

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