The response of nonlinear, second-order systems is examined from a new point of view which greatly simplifies presentation of the usual frequency-response diagrams. The use of “natural” forcing functions results in a general equation relating the maximum amplitude of the applied force to the maximum amplitude of the restoring force. The relationship is found to be a function of the ratio of the period of free oscillation to the period of the forcing function. The results apply for any second-order system without damping and with a nonlinear (or linear) restoring force. The special cases of a linear system and of Duffing’s equation are considered to illustrate similarities as well as differences between treatment of linear and nonlinear frequency-response problems.

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