Various loss factors of a master harmonic oscillator coupled to a number of satellite harmonic oscillators

Abstract

Three loss factors are defined for a master harmonic oscillator (HO); the I-loss factor, the U-loss factor, and the effective loss factor. A conductance (β) is conventionally defined as the ratio of the power imparted to a dynamic system by an external drive to the stored energy that this input power generates. The conductance (β) is related to the loss factor (η) by the frequency (ω); β=(ωη). In light of this definition, it is shown that all three loss factors are identical for an isolated master HO at resonance. Differences arise among these loss factors when the master HO is coupled to satellite harmonic oscillators (HO’s). The first two loss factors retain their definitive format in the sense that the stored energy is reckoned only in the master HO; the energy stored in the coupled satellite HO’s and in the couplings is discounted. The effective loss factor, on the other hand, is defined by accounting for the total stored energy that the external drive applied to the master HO generates in the complex. The complex here is composed of the master HO, the satellite HO’s, and the in situ couplings. In those situations in which the portion of the total energy stored in the satellite HO’s and in the couplings substantially exceeds the stored energy in the master HO, the I-loss factor and the U-loss factor may substantially exaggerate the true loss factor of the coupled master HO. Situations of this type are illustrated by data obtained in computational experiments, and it is argued that the true loss factor of the master HO in the complex as a whole is the effective loss factor.