On damped linear dynamical systems

Abstract

This paper is concerned with damped linear dynamical systems which fail to satisfy the so-called "convenience hypothesis", an assumption that guarantees the existence of classical normal modes. Under suitable conditions, estimates are given for the error committed when such a system is described approximately by a differential equation which does satisfy the convenience hypothesis. One of these estimates is used to derive an upper bound on the frequency response of systems which do not violate the convenience hypothesis too severely.

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