That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks.
The best one is turbulence in nonlinear equations. You can make a model of this by coupling a collection of independent HO's with weak nonlinearities, and ask how the energy cascades from the low frequency modes to the high frequency modes. You can solve this numerically, or with different approximation techniques, and this is a problem of current research interest, easily accessible to undergraduates.
See Paradoxical behaviour of mechanical and electrical networks. The experiment can be setup easily and illustrates the idea of effective spring constants in situations when the oscillators are coupled in series or parallel.