International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 29 |Article ID 213152 | https://doi.org/10.1155/S0161171202006014

J. N. Boyd, R. G. Hudepohl, P. N. Raychowdhury, "Breaking the symmetry of a circular system of coupled harmonic oscillators", International Journal of Mathematics and Mathematical Sciences, vol. 29, Article ID 213152, 10 pages, 2002. https://doi.org/10.1155/S0161171202006014

Breaking the symmetry of a circular system of coupled harmonic oscillators

Received23 Oct 2000

Abstract

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6 particles are given.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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