Damped Single Degree-of-Freedom System

Abstract

We have seen in the preceding chapter that the simple oscillator under idealized conditions of no damping, once excited, will oscillate indefinitely with a constant amplitude at its natural frequency. However, experience shows that it is not possible to have a device that vibrates under these ideal conditions. Forces designated as frictional or damping forces are always present in any physical system undergoing motion. These forces dissipate energy; more precisely, the unavoidable presence of these frictional forces constitute a mechanism through which the mechanical energy of the system, kinetic or potential energy, is transformed to other forms of energy such as heat. The mechanism of this energy transformation or dissipation is quite complex and is not completely understood at this time. In order to account for these dissipative forces in the analysis of dynamic systems, it is necessary to make some assumptions about these forces, on the basis of experience.