Breaking the symmetry of a circular system of coupled harmonic oscillators
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202006014 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |