As indicated in the Preface, it is assumed that the reader is familiar with the content of a typical introductory course in mechanics that includes a discussion of the basics of the harmonic oscillator. It is an essential element in acoustics and it will be reviewed and extended in this chapter. The extension involves mainly technical aspects which are convenient for problem solving. Thus, the use of complex variables, in particular the complex amplitude, is introduced as a convenemt and powerful way of dealing with oscillations and waves.

With modern digital instrumentation, many aspects of signal processing are readily made available and to be able to fully appreciate them, it is essential to have some knowledge of the associated mathematics. Thus, Fourier series and Fourier transforms, correlation functions, spectra and spectrum analysis are discussed. As an example, the response of an oscillator to a completely random driving force is determined. This material is discussed in Section 2.6. However, it can be skipped at a first reading without a lack of continuity.

The material referred to above is all standard ; it is important to realize, though, that it is generally assumed that the oscillators involved and the related equations of motion are linear. This is an idealization, and is valid, at best, for small amplitudes of oscillations. But even for small amplitudes, an oscillator can be non-linear, and we end this chapter with a simple example. It involves a damped mass-spring oscillator. Normally, the friction force is tactily assumed to be...