Which Residual Mode Captures the Energy of the Dominating Mode in Second Order Hamiltonian Systems?

Motivated by the instability of suspension bridges, we consider a class of second order Hamiltonian systems where one component initially holds almost all the energy of the system. We show that if the total energy is sufficiently small then it remains on this component, whereas if the total energy is larger it may transfer to the other components. Through Mathieu equations we explain the precise mechanism which governs the energy transfer.