Vibrations

Abstract

It is probably safe to assume that we all know what is meant by a vibration, whether we think of sitting on a bus, experiencing the rattles and bumps as it struggles uphill, or the twang of a guitar string. The essential ingredient common to all vibrations is the to-and-fro motion, without there being any overall movement in any direction. This chapter will enable us to under-stand more about all types of vibrations. Engineers need to understand many things that oscillate; a few examples are engines, buildings subject to high winds, offshore structures and output from electrical circuits (for example hi-fi systems). At first sight, all of these seem very different, and very difficult to model. However, if attention is focussed on the end product, they all exhibit a to-and-fro motion, and it is this that we will use Newton’s laws to describe. We will restrict our attention to motion in one dimension, or, more strictly, to a single degree of freedom.