This paper presents methods for determining the exact solutions of certain two-degree-of-freedom nonlinear systems with high-degree polynomial restoring forces. The exact solutions are the normal modes of the systems. A stability analysis of solutions in the normal modes is given. Some systems have normal modes whose stability is a function of amplitude. The stability of complicated systems can be approximated by superposing the stability characteristics of simpler systems. Some experimental confirmation by analog computer is also presented.

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