Abstract
The vibration of a chain, fixed one end to a rotating disc and having a concentrated mass at the other end in the field of centrifugal force, is dealt with as a boundary problem. The analytical results are exactly equal to those of the experiments, and will be shown as follows : a) The larger the intensity of the field becomes, the larger becomes the frequency of a chain. b) The larger the mass ratio M/m of chain m to concentrated mass M becomes, the less becomes the frequency. c) The frequency extends one of a mathematical pendulum in the case of a mass ratio M/m is over twenty. In addition, the author calculated Legendre's polynomials of the 2nd kind from 0th to 7th degree.
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