Loss factors of a complex composed of a number of coupled harmonic oscillators

Abstract

Investigation of the response of a complex composed of a number of coupled harmonic oscillators is conducted. One of the harmonic oscillators is designed as the master, the others as the satellites. The expression for the loss factor of the coupled master harmonic oscillator is sought. Two distinct loss factors are defined; the prevailing loss factor and the effective loss factor. The first is defined in terms of the real part of the inverse of the normalized in situ admittance of the master harmonic oscillator. The second is defined in terms of the ratio of the normalized input power onto the master harmonic oscillator to the normalized stored energy in the complex due to that power injection. The relationship and the contrast between these two loss factors are revealed. It is argued that, with the exception of an isolated master harmonic oscillator, the prevailing loss factor is apparent; it is the effective loss factor that is real. Whereas the prevailing loss factor invokes the question, ‘‘Where did the energy go?,’’ the effective loss factor renders this question moot.