program to simulate the transient behaviour of a simple pendulum and to create an animation of it s motion

Step wise Explanation of code

• First i given the input values ,intical conditions and time interval.
• The simple pendulum equation is an second order ode.so i splitted it into two first order ode\'s .
• i created a matlab function which is used in solving the ode.
• Then using ode45 solver i solved the second order ode .
• next i plotted figure 1 which tells us the transient behaviour of the simple pendulum.
• next step is to create the animation of the simple pendulum
• we have to calculate end point of the pendulum by using the for loop in order to get animation
• first plot the end point of the pendulum using marker and add axis limits
• next by using the line command we plot a line of simple pendulum
• by using title and num2str command we keep the title and the time of the animation
• to get a movie we have to use getframe which gets the images of the plot and combine all images to look like ananimation
• in the last we save the video in the desired format.

Errors Facing While programming

i got a lot of errors while programming the animation part

the first wrong i did is that i did not used the for loop and went in a different approach by using the angles then i realized that it is wrong.then i again whatched the video of robot arm kinematics the first challenge from that video i started using the for loop and the getframe commands for how to animate.

the second big errors i got in the execution of the for loop for finding the end points of the simple pendulum it took me a long time i referred the documentation that matlab provides and some videos from that i finally got executed the for loop

the next problem is in plotting the values.first i directly ploted the pendulum line using the line command and the marker then the animation is coming but the images are not removing.then i again ploted only the point and gave axis limits then i plotted then i plottedcthe2 line then the animation worked fine.

almost it took 2 days for me to sove this challenge.

clear all
close all
clc
% inputs
b=0.05;
g=9.81;
l=1;
m=1;

% initial condiations
theta_0 = [0;3];

% time points
t_span = linspace(0,20,500); %time interval

% ode solving
[t, results] = ode45(@(t,theta) ode_func(t, theta,b,g,l,m),t_span, theta_0);

figure(1)
axis([0 12 -3 3]);
plot(t,results(:,1))
hold on
plot(t,results(:,2))
xlabel(\'time\')
ylabel(\'plot\')

o = [0 0]; % origin point for pendulum 

% loop for animation
for i =1:length(t)
    % end point for pendulum
    x(i) = l*sin(results(i,1));
    y(i) = -l*cos(results(i,1));
    %pendulum line
    figure(2)
    plot(x(i),y(i),\'.\',\'markersize\',60); 
    axis([-1.05 1.05  -1.5 0.2]);%axis limit
    line([o(1) x(i)], [o(2) y(i)],\'color\',\'r\',\'Linewidth\',2);
    title([\'PENDULUM MOTION at T =\',num2str(i*(20/500)), \'s\']);% pendulum motion for 20 seconds
    f= getframe; % captures the images and form a movie
    
end
    v = VideoWriter(\'ode_2nd_order_pendulum.avi\',\'Uncompressed AVI\'); % saves the video
    open(v);
    writeVideo(v,f); % read the video file
    close(v);