DIDACTIC ASPECTS OF PHYSICS FOR ENGINEERS: NON-LINEAR OSCILLATIONS

Abstract

It is well known that oscillations as a physicalphenomenon occupies a large area in engineering practice.Not a single engineering construction can be realizedwithout taking into consideration natural mechanical orelectrical vibrations. However, it is quite common inteaching experience to consider simple harmonic, dying andforced oscillations only. Non-linear oscillations (parametricor self-sustained) are normally disregarded or mentionedwithout any serious analysis because of complicatedmathematical equations which describe non-linearprocesses. Nevertheless, their importance can hardly beoverestimated since almost any real engineering designdeals with non-linear oscillations. Some simple examplesare considered in a rather qualitative manner but notneglecting mathematics. For parametric oscillations, theinflux of external energy is analyzed using a simple circuitwith a capacitor whose capacity is modulated by externalforce. It is shown how the mathematics can be simplified forthe sake of understanding of basic physical principles.

Index Terms - Non-linear oscillations, parametricoscillations, self-sustained oscillations, self-maintainedoscillations.