Oscillations of Mechanical and Electrical Systems

Abstract

The equation of motion for a mechanical system comprised of a mass at the end of a string and vibrating in a viscous medium is compared to the analogous equation for an electrical system consisting of an R-L-C circuit. The distinction between natural and driven dynamics is carefully drawn. For natural motion the initial value problem is solved for the case of negligible viscous damping, negligible electrical resistance. The resonance phenomenon is brought out fully in connection with the analysis of forced motion, and the characteristics of resonance are related to those of natural motion, attention being drawn to the quality factor Q. A subsequent section is then devoted to an explanation of the operation of oscillators in general, and extended to a description of an actual pendulum clock. In the problems we treat natural motion for nonnegligible damping, and also introduce the Green’s function method of finding forced motion solutions.