Hi Michael
I understand that you are facing an issue while plotting movement of a driven damed pendulum where the returned graph deviates from the expected graph. I assume that you are referring to the second graph in this article: https://galileoandeinstein.phys.virginia.edu/7010/CM_22a_Period_Doubling_Chaos.html
I base this answer on the information provided in the above article.
Upon a careful review of your code and the shared article, I believe the constant definitions or values can be revised. Additionally, according to the graph shown, the initial conditions for the pendulum are "[0 0]" since the angluar displacement (phi) at t=0 is 0.
For your reference, I am attaching a code with this answer to plot the movement of a driven damed pendulum. Kindly change the constants as per your setup.
clear all;
gamma=1.06;
w0 = 1.5;
w = 1;
beta = 0.75/2;
% declare a sym system
syms t phi(t)
eqn = diff(phi,2) + 2*beta*diff(phi,1) + w0^2*sin(phi) == gamma*w0^2*cos(w*t);
[V] = odeToVectorField(eqn)
M = matlabFunction(V,'vars', {'t','Y'})
sol = ode45(M, [0 100], [0 0])
plot(sol.x, sol.y(1,:))
grid on
The resulting plot matches the given expected plot.
Hope this helps.
Regards,
Nipun
