Small oscillations and closed orbit

[bznm]

Homework Statement

I'm studying small oscillations. When can I say that an orbit is closed?

The Attempt at a Solution

I remember that there is a ratio that must be a rational number but I don't remember other thing...
Thank you!

 

[Coelum]

An orbit is closed if, after a finite number of revolutions, the point returns to its initial position. Now, impose that condition to the unperturbed orbit and the oscillation...