Week 3 - Solving second order ODEs

now, we are going to slove the second order ODE

in the first step the basic program should be type in the editor windoe

and then the input are fed in the program is called geomentry parameters.like, mass, length, damping, gravity.

Ater that the initial condition should be fed into the editor window

the displacement and velocity and also time span also feeded into the initail condition

once the initial condition is over then,

after that open the new file and the fuction to fin (dtheta/dt)

function is used to declare function and input and output. the function of the matlab is procced in the oargram is fed into the the ode program

and then jumping back into the ode program now the fuction is same on the workspace

after that now we are going to find the ode contion

that mean t and output.

(t,output) is required the separate formula

[t,output] = ode45(@(t,theta)ode_pen(t,theta,b,g,l,m),t_span,dis_v)

this is the formula for to find (t, output)

and then the program run is successful then you continue withj plotting.

plotting

plot is ued to connecting the twon line the vector of x,y and of the pendulam is rotating the bar of the revalution the of the pendulam

for code is used for theta,s

for loops is used repaet the loops again and again and for the roataing the movemnt is calculated the angular velocity

and then mark the plotting the figure is placed on the window after that move on to pendular diagram

that is figure 2

in the figure 2 plot the pendular diagram and animated the velocity of the diagram in plot the axis in the graph frame and the linewidth is mension as the required dimension and control the video speed as per the required and end the for programm

and the next process is to create the animation video and same

the same procedure is create the animation program

movie cod eis typed and the after that the video format and place the name for the avi and run program and same on the matlab file

pendulam animation link;

https://drive.google.com/file/d/1NEL_Sl1oBJPg6SVmttDzc7GKCmwutOE3/view?usp=sharing

error

the code is worng i used the lowe case letter

after i uderstand

function [dtheta_dt]=ode_pen(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

---------------------------------------------------------
clear all
close all
clc

%input 
l=1
m=0.2
g=9.81
b=0.05
ct=1
%initial condition

dis_v=[0;5]
t_span=linspace(0,20,150);

%ode condition 
[t,output] = ode45(@(t,theta)ode_pen(t,theta,b,g,l,m),t_span,dis_v)

figure(1)
hold on
plot(t,output(:,1))
plot(t,output(:,2))
xlabel('x-axis')
ylabel('y-axis')
title('variation of angle displacementamd angular velocity w.r.t time','color','r')

theta2=output(:,1);

for i=1:length(theta2);
    theta_x= theta2(i);
    
    x0=0;
    y0=0;
    
    
    y1=-l*cos(theta_x);
    
    %plotting the pendulam
    figure(2)
    plot([-0.5 0.5],[0 0],'color','b','linewidth',5,'color',[rand rand rand])
    hold on
    plot([x0 x1],[y0 y1],'color','r','linewidth',2,'color','b')
    hold on
    plot(x1,y1,'o','markers',15,'markerfacecolor','r')
    hold off
    grid on
    axis([-1.5 1.5 -1.5 0.5]);
    pause (0.02)
    M(ct)=getframe(gcf)
    ct=ct+1
    
end
movie(M)
 videofile=VideoWriter('pendulum.avi','uncompressed avi');
 
 open(videofile)
 writeVideo(videofile,M)
 close(videofile)

my mistake and corrected