Coupled oscillators and normal modes — A.P. French
Physics — Waves · forced-oscillations-energy
Problem
Consider a system with a damping force undergoing forced oscillations at an angular frequency ω.
(a) What is the instantaneous kinetic energy of the system?
(b) What is the instantaneous potential energy of the system?
(c) What is the ratio of the average kinetic energy to the average potential energy? Express the answer in terms of the ratio ω/ω0.
(d) For what value(s) of ω are the average kinetic energy and the average potential energy equal? What is the total energy of the system under these conditions?
(e) How does the total energy of the system vary with time for an arbitrary value of ω? For what value(s) of ω is the total energy constant in time?