Simple Vibration

Abstract

This programme is concerned with the analysis of some simple vibrating systems. They will all be examples of what is called Free Undamped Response. This term will be explained later. This subject is important in many branches of engineering: mechanical systems vibrate, buildings and structures vibrate, and electrical circuits oscillate. (‘Oscillation’ is just another word for vibration.) You will deal more thoroughly with the subject later in your course. Moreover, vibration analysis forms an excellent discipline for the analysis of mechanical system generally. You should find that writing the correct equation of motion for a vibrating system will reinforce your understanding of other dynamics problems. The programme comes at the end of the book because it calls upon various principles established in earlier programmes. You will find that we shall make use of work done in Programmes 1, 5, 6, 7 and 9. Referring to Programme 5 in particular, be clear at the outset that vibration is a case of variable acceleration. So never be tempted in this programme to make use of the well-known kinematic equations of Programme 1, Frame 48.