Chapter 14 - OSCILLATORY MOTION

Abstract

Vibrational, or oscillatory, motion is important because it is common and is a basic constituent of wave motion. This chapter forms a bridge between the mechanics of particles and rigid bodies and the physics of wave motion. It focuses on one-dimensional systems—the systems whose motion can be described by a single linear or angular variable. In each system, the displacement— whether linear or angular—varies sinusoidally with time. The sine and cosine functions are called harmonic functions, and this type of motion is referred to as simple harmonic motion (SHM). The chapter demonstrates that a system executes SHM if its acceleration and displacement are directly proportional but in opposite directions. It has been shown that SHM describes the motion projected on a diameter of an object engaged in uniform circular motion. The chapter further describes the transient behavior of a harmonic oscillator that is subjected to a dampening mechanism. A damping mechanism converts the mechanical energy of an oscillator into thermal or other non-mechanical forms of energy. The chapter also discusses the steady-state response of a damped oscillator to a sinusoidal driving force.