The simple harmonic oscillator, driven by a sinusoidally varying force, is central to the discussion of vibrating systems, being a model for so many real systems and therefore serving to unify the description of very diverse physical problems. In view of this it is worth spending some time examining it from several different aspects, even though it might be thought that a formal solution of the equation of motion contained everything useful to be said on the matter. Indeed, if one were concerned only with physical systems that could be modelled exactly in these terms a single comprehensive treatment would suffice for all. Real systems, however, normally only approximate to this idealization, and alternative approaches may then prove their worth in allowing the behaviour to be apprehended semiintuitively, often enough with sufficient exactitude to make mathematical analysis unnecessary. The reader who has progressed to this point will be familiar enough with the most elementary analyses not to be worried that we approach the problem indirectly, picking up an argument that has already been partially developed. More familiar treatments will be introduced in due course.

Transfer function, compliance, susceptibility, admittance, impedance

The essential framework for this approach has already been laid down in chapter 5, where the concept of the transfer function χ(ω) was introduced. We had in mind there a linear transducer into which a sinusoidal signal A e−iωt was fed, and from which emerged an output signal χ(ω) A e−iωt.