A Demonstration of the Spring-Mass Correction

Abstract

The frequency of oscillation of a body of mass m, suspended from a coil spring of mass M and force constant K, is the same as that of a body of mass m* = m+pM, suspended from a mass-less spring of the same force constant. It is shown that the factor p varies from 13, when m≫M, to π2/4 = 0.41 when m≪M. The wave apparatus consisting of a flat steel strip having equally spaced cross-arms is an equivalent system, and the factor corresponding to the mass ratio m/M can be varied over a considerable range by replacing the lowest cross-arm with a rod to which counterweights can be attached.