Dynamics of Harmonically Bound Semi-Infinite and Infinite Chains with Friction and Applied Forces

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Abstract
The dynamics of semi‐infinite and infinite linear chains of identical masses and ideal springs is studied. In addition to the harmonic coupling between nearest neighbors, each particle is harmonically bound to ts equilibrium position and is subject to friction and time‐dependent applied forces. The Laplace transform method is used to express the motion of all the particles. The exact solutions are found and discussed for four different cases: (a) an infinite chain, (b) a semi‐infinite chain, (c) a semi‐infinite chain with the position of the end particle specified as a function of time, and (d) an infinite chain with the position of one particle specified as a function of time. By specializing some results of the present work, those of previous calculations on simpler systems by other authors are recovered.

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