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This paper treats the analysis of nonlinear systems having more than a single degree of freedom. The method used is the Ritz or Ritz- Galerkin, which has been extensively applied to statical problems in elasticity and to eigenvalue problems of various types. Until very re- cently, however, it has rarely been applied to dynamical problems other than eigenvalue ones. As shown by some specific examples, the method proves to be a powerful one for the purposes at hand.