I'm not sure if this is the right spot to post this question, but I figured since this is the differential equations section and this question from from my differential equations textbook..I'd post here.
The question asks: "For the nonlinear damped pendulum, show that for every integer n and every angle theta_0 there is an initial condition (theta_0, v_0) whose solution corresponds to the pendulum moving around the circle at least n times, but not n+1 time, before settling down to the rest position."
The professor hasn't gone over this yet, so I'm not too sure where to start. Does it have to do with hamiltonian systems?