Free and Damped Oscillations

Abstract

This chapter introduces several equivalent mathematical expressions for the oscillation of a physical system and shows how one expression can be transformed into another. The expressions involve the following concepts: amplitude, frequency and phase. The motion of a mass attached to one end of a spring is described by Newton’s laws. The resulting second-order homogeneous differential equation has three solutions, depending on the extent of energy loss (damping). The difference between a general and a particular solution is discussed, as well as superposition of solutions for linear and nonlinear equations. Oscillation in an electrical RCL circuit is discussed, and energy conservation in an oscillating system which has no energy dissipation is examined.