Document Type
Article
Original Publication Date
2002
Journal/Book/Conference Title
International Journal of Mathematics and Mathematical Sciences
Volume
29
Issue
11
DOI of Original Publication
10.1155/S0161171202006014
Date of Submission
August 2014
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 6particles are given.
Rights
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.
Is Part Of
VCU Mathematics and Applied Mathematics Publications
Comments
Originally published at
http://dx.doi.org/10.1155/S0161171202006014