A Damping Ratio Bound for Networks of Masses and Springs

The damping ratio is a key performance measure in systems that can be modelled as networks of masses and springs. We derive a lower bound on this quantity that applies to such networks when the masses are subject to viscous damping. The result allows the size of the damping ratio to be understood as a function of the system parameters. We use this to derive a decentralised criterion which, if satisfied, guarantees that all the modes of a swing equation power system model are sufficiently well damped, independently of its operating point and size.