Steidel's extension of Rayleigh's method for calculating the natural vibrational frequencies of mechanical systems with two degrees of freedom provides an elegant method to obtain exact results. In the present article this approach, which perhaps has not been exploited as much as it could be, is first reviewed and then several examples of the procedure are given. An extension of the method to three degrees of freedom is presented, and a natural generalization of Rayleigh's principle is suggested.
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