Given point-masses connected by loss-less springs and a specific initial kinetic energy distribution.
What mathematical tools exist to analyze the system for resonance stabilization.
This problem becomes complex because of the kinetic-energy range, which is constantly in flux or shifting from one point-mass to another.
No doubt the resonance stabilization depends on the energy range as well as the specific locations of that kinetic energy (KE) within the mass-spring system. Some KE level will bring two particles into resonance and then connected spring systems will act as forcing or dampening agents... So there seems to be a more primitive question: How will a dynamic system respond to a given initial energy distribution from a statistical perspective as it relates to an "average" behavior of a given point-mass and its neighbors.
I am seeking an approach to this problem that will be general enough to apply to any mass-spring system.