Propagation of a Disturbance in a Chain of Interacting Harmonic Oscillators

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Abstract
The exponential Fourier transform method is used to study the propagation of a general disturbance along a semi-infinite chain of interacting harmonic oscillators. In addition to the harmonic coupling between nearest neighbors in simple chains, each particle is bound to its equilibrium position by an ideal spring. In contrast with previous studies on simple chains, the initial conditions (at t=0) are not specified, and the motion of all the oscillators is expressed in terms of either the specified time-dependent displacement of the end particle or the specified time-dependent external force applied to it. The inverse transforms not readily available from tables are obtained by carrying out the inversion integrals explicitly in the complex frequency plane. By specializing some results of the present work, those of previous calculations on simple chains are recovered.

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