Abstract
The venerable problem is considered of finding the natural frequencies of small oscillations about the equilibrium configuration of a suspended chain, under the assumptions of a continuous, perfectly flexible, inextensible, and lossless chain, supported at two fixed endpoints in a uniform gravitational field. A variety of analytical, variational, and numerical methods gives results that are valid over the full range of chain span-to-length ratios, including the limiting cases of very slack and very taut chains. Some surprising predictions of the theory are confirmed by experimental data.
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