Period of the DE trajectory

[srpvx]

I have a second order nonlinear ODE. I know that a trajectory with specified initial conditions \left[ x(0) = x_0, \dot{x}(0) = \dot{x}_0 \right] is periodic. How can I numerically calculate period of this trajectory without solve this DE?

[rcgldr]

Are you allowed to use a numerical method like Runge Kutta or would that be considered "solving" the ODE?

[srpvx]

Are you allowed to use a numerical method like Runge Kutta or would that be considered "solving" the ODE? I mean that the numerical solution like the attachment paper.

[rcgldr]

That's a method that I'm not familiar with. Hopefully someone here may be able to help.