Week 3 - Solving second order ODEs

aim

to write a program that solves the ode and to animate the motion of pendulum.

procedure

1.take the input values and conditions

2.convertion of 2nd order to first order ode

3.create a function ode

4.create a simple pendulum progtram using the created ode function

5.with a time span of 20 seconds with 500 steps.

6.solving function by using ode45

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

dis_angvelo=[0;3];
t_span=linspace(0,20,500);
[t,results]=ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,dis_angvelo);
figure(1)

plot(t,results(:,1),'linewidth',1)
hold on
plot(t,results(:,2),'linewidth',1)
axis([0 25 -3 3])
xlabel('Time - sec')
ylabel('Angular Velocity&Displacement')
legend('change in dispacement','change in angular velocity')
hold off

figure(2)
plot(results(:,1),results(:,2))
xlabel('Position-rad')
ylabel('Angular Velocity-rad/sec')
theta2=results(:,1)
ct=1
for i=1:length(theta2)
theta3=theta2(i);

x0=0;
y0=0;
x1=l*sin(theta3);
y1=-l*cos(theta3);

figure(3)
plot([-1.1 1.1],[0 0],'linewidth',2);
hold on
plot([x0 x1],[y0 y1],'color','r','linewidth',2)
hold on
plot(x1,y1,'o','markers',20,'markerfacecolor','b')
hold off
grid on
axis([-1.5 1.5 -1.5 1]);
Angular_Displacement=results(i,1)
Angular_Velocity=results(i,2);
txt1=['Angular Displacement : ' num2str(Angular_Displacement) 'rad'];
txt2=['Angular Velocity: ' num2str(Angular_Velocity) 'rad/s'];
text(-0.5,0.5,3,txt1,'color','r')
text(-0.5,0.2,3,txt2,'color','b')
pause(0.003)
M(ct)=getframe(gcf);
ct=ct+1;
end

movie(M)
videofile=VideoWriter('pendulum.avi','MPEG-4');
open(videofile)
writeVideo(videofile,M)
close(videofile)

function 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)*theta(2)-(g/1)*sin(theta(1));
 dtheta_dt=[dtheta1_dt; dtheta2_dt];
 
    
    end

plot

video link for the pendulum simulation

https://drive.google.com/file/d/1Y2_t-zEaPZFMdddU_UEeCXQRz0UjTMcw/view?usp=sharing

conclusion

plot is shown of how the displacement and angular velocity change with respect to time.

errors faced

removed the inverted commas for the number after the line width