It's simply* two simple harmonic oscillators, coupled. The energy swaps back and forth between the available modes, and the rate at which this happens is the oscillation frequency times the coupling coefficient (more or less).
*For some degree of "simple". In this case, you'd have to know dynamics for it to be "simple", which... it's undergrad level, but it's not something trivial and obvious if you've not been to school. So, there's that.
(Also, the motion isn't exactly SHM, it's continuous rotation; the dynamics are similar enough that I think this is explanatory, but I wouldn't bet much on this explanation until I've seen a more involved proof.)
Related viewing:
However, IIRC they cover the trajectory (which combinations of rotations are allowed), but NOT the rate of transition from one orientation to the next, which requires some more explanatory power (I think it might be hard if not impossible to avoid dynamics in that case, since after all, that's, well, the dynamics of the object's motion!).
Tim