International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 11, Pages 665-674

Breaking the symmetry of a circular system of coupled harmonic oscillators

J. N. Boyd, R. G. Hudepohl, and P. N. Raychowdhury

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, VA, USA

Received 23 October 2000

Copyright © 2002 J. N. Boyd et al. 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.


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.