MOTION STUDY OF PENDULUM

1. AIM: Program to simulate the transient behaviour of a simple pendulum and to create an animation of it\'s motion.

1. Governing Equation :

1. OBJECTIVE OF PROJECT: To To study how the time period of a simple pendulum .

changes when its amplitude (θ ) is changed.

1. Body :

   clear all
   close all
   clc
   
   b=0.05;
   g=9.81;
   l=1;
   m=1;
   
   ct = 1;
   %initial  condition
   %initial displacement of pendulum is zero
   %we give intial angular velocity #rad/sec.
   
   theta_0 = [0;3];
   %time points
   
   t_span = linspace(0,20,500);
   
   %Solve ODE
   
   [t,result] = ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);
   
    %here we sub plot
   
   subplot(5,4,[13,14,17,18]);
   plot(t,result(:,1),\'color\',\'b\');
   hold on;
   plot(t,result(:,2),\'color\',\'g\');
   
   hold off;
   subplot(5,4,[15,16,19,20]);
   plot(result(:,1),result(:,2));
   
   ylabel(\'plot\')
   xlabel(\'time\')
   
   legend(\'Displacement\',\'velocity\')
   
   
   %Animation For Pendulum
   
   ct = 1;
   
   for i=1:length(result(:,1))
     x0 = 0;
     y0 = 0;
     
     x1 = l*sin(result(i,1));
     y1 = -(l*cos(result(i,1)));
     subplot(5,4,[1,2,3,4,5,6,7,8,9,10,11,12]);
     
     plot([-1 1],[0 0],\'linewidth\',4 ,\'color\',\'k\');
     hold on
     
      line([x0 x1],[y0 y1],\'linewidth\',3,\'color\',\'b\');
      
    
      hold on;
      
      plot(x1,y1,\'-o\',\'markers\',20,\'markerfacecolor\',\'g\');
      
      grid on
      axis ([-1.5 1.5 -1.5 0.5])
      pause(0.03);
      hold off
      
      text = sprintf(\'pendulum%d.png\',ct);
      saveas(1,text)
      ct=ct+1;
   
   end

   YOUTUBE LINK FOR SIMULATION

https://youtu.be/8lth_BgifXc

Function that is used avove Programme with name ode_func.

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
 

1. CONCLUSION

1. From getting a simulation result clear the concept of Simple Pendulum.
2. ALso gave how avobe equation is important to getting a result
3. its show hoe time and amplitude depand