Question about nonlinear techniques

[borkborkmath]

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?

 

[Deleted member 4993]

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?

What is the equation of motion of "the nonlinear damped pendulum"?

 

[borkborkmath]

theta' = v
v' = -bv - sin(theta) ?