Falling Coupled Oscillators & Trigonometric Sums

S. R. Holcombe

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arXiv · 1612.09317

Falling Coupled Oscillators & Trigonometric Sums

S. R. Holcombe

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Abstract

A method for evaluating finite trigonometric summations is applied to a system of N coupled oscillators under acceleration. Initial motion of the nth particle is shown to be of the order ${{T}^{2n+2}}$ for small time T and the end particle in the continuum limit is shown to initially remain stationary for the time it takes a wavefront to reach it. The average velocities of particles at the ends of the system are shown to take discrete values in a step-like manner.

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S. R. Holcombe. 2016-12-21. Falling Coupled Oscillators & Trigonometric Sums. https://arxiv.org/abs/1612.09317

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