Solving Second Order ODE - Pendulum_Dampless

Pendulum_No_Damping Main Code

clear all;
close all;
clc;

%input variabes
g = 9.81; % m/s^2
l = 1; %m
m = 0.5; %kg
w = g/(m*l);

%initial conditions
theta_initial = [0; 10];

%time condition
time1 = linspace(0,0.5,500);

[t, results] = ode45(@(t, theta) ode_func(t, theta, w), time1, theta_initial);

figure(1)
plot(t, results(:, 1));
hold on;
plot(t, results(:, 2));
xlabel("Time");
ylabel("Velocity and Displacement"); 

figure(2);
O = [0 0];
axis(gca, 'equal');
axis([-1 1 -2 2]);
grid on;

for i=1:length(t)
    %mass point
    P = l*[sin(results(i,1)) -cos(results(i,1))];
    %draw circle
    %O_circ = viscircles(O, 0.1);
    
    %pendulum rope line
    pend = line([O(1) P(1)], [O(2) P(2)]);
    %ball
    ball = viscircles(P, 0.1);
    
    %time interval
    pause(0.001);
    
    if i<length(t)
        delete(pend);
        delete(ball);
        %delete(O_circ);
    end
   
end    

ODE Solver Code- File Name: ode_func

function [dtheta_dt] = ode_func(t, theta, w)
  theta1 = theta(1);
  theta2 = theta(2);
  dtheta1_dt = theta2;
  dtheta2_dt = -(w^2)*sin(theta1);
  dtheta_dt = [dtheta1_dt; dtheta2_dt];
end

The given dampling less equation of the pendulum is solved and simuated. The youtube video link for the simulaiton is:

https://youtu.be/hXYRFv41uKw

Images of Program Run:

1. Image depicting the velocity(Red curve) and displacement(Blue curve)of the pendulum motion.

2. Image during simulation of pendulum motion.