In this paper, a method of eigen-analysis for a vibrating elastic system is presented. The model analyzed is a Bernoulli-Euler beam having a slender payload at the free end and being attached at the other end to a compliant, rotating hub. The system equations with the complete boundary conditions are derived. The corresponding frequency equation in a dimensionless form is solved by using the secant method. Agreement with other works not only verifies the accuracy of the results, but also demonstrates the generality of the model.

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