Graphing a nonlinear 2nd order differential equation?

I've searched around for a similar solution to what I'm looking for but I'm terrible at debugging. I need to graph this nonlinear 2nd order differential equation:

g = 9.81

m = 15000/g

L = 1.5 meters

J = m*L^2

J*theta_dd + m*L*g*sin(theta) = 0

Answer 1

[Ameer Hamza]

See ode45(): https://www.mathworks.com/help/matlab/ref/ode45.html espically the example titled "Solve Nonstiff Equation".

IC = [1; 0]; % initial condition
tspan = [0 10];
[t, theta] = ode45(@odefun, tspan, IC);

plot(t, theta);
legend({'$\theta$', '$\dot\theta$'}, 'FontSize', 16, 'Interpreter', 'latex');

function dtheta = odefun(t, theta)
    % theta(1) = theta, theta(2) = theta_dot

    g = 9.81;
    m = 15000/g;
    L = 1.5;
    J = m*L^2;
    
    dtheta1 = theta(2);
    dtheta2 = -m*L*g*sin(theta(1))/J;
    dtheta = [dtheta1; dtheta2];
end

[Daniel Keith]

Thank you!

[Ameer Hamza]

I am glad to be of help!!!