I can't find where the mistake is. Could anyone help me with my code?

Differential equation of simple pendulum

d^2θ /dt^2 + (g/L)*sin(θ )=0

Initial conditions: θ(0) = θ0 , θ'(0) = 0

The angular displacement θ0 = 30 degrees, length of the pendulum L = 0.6 m and gravity g = 9.82 m/s^2.

This is the script I use to solve the differential equation with ode45 and to plot the solution in degrees but I got a wrong plotting.

theta0=30;
L=0.6;
g=9.82;
t=0:100;
[t,theta30]=ode45(@(t,THETA) fun(t,THETA,g,L),t,[theta0*pi/180 0]);
plot(t,theta30(:,1)*180/pi,'--b')
grid on
axis ([0 t(end) -30 30])
xlabel('Time')
ylabel('Angle')
function dthetadt=fun(t,THETA,g,L)
dthetadt=zeros(2,1);
dthetadt(1)=THETA(2);
dthetadt(2)=(-g/L)*sin(THETA(1));
end

Answer 1

[Stephan]

Hi,

the way you define t is not useful. Use:

t = [0 100]

What you do is corresponding to a sample rate of 1 second. This lets the solution appear wrong, due to the ratio of frequency of your pendulum and the 1 second sample rate for plotting.

Best regards

Stephan