Graphing the movement of a driven damed pendulum

I'm trying to graph the movement of a driven damped pendulum, whose equation of motion is :

I should get something like this :

but with my code I'm getting this: what am I doing wrong?

clear all
gamma=1.06;
g=9.81;L=0.5;m=1;dair=1.225;muair=1.81e-5;R=0.1;                            
w02=g/L;b=6*pi*dair*muair*R; beta2=b/m;                                                
w=2/3*sqrt(w02);                                                            
syms y(t)
[V] = odeToVectorField(diff(y, 2) == gamma*w02*cos(w*t)-beta2*diff(y)-w02*sin(y)); 
M = matlabFunction(V,'vars', {'t','Y'});
[time,A] = ode45(M,[0 200],[-pi/2 0]);
figure
plot(time,A(:,1))
figure
plot(time,A(:,2))

Answer 1

[Nipun]

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