A classical iteration procedure valid for certain strongly nonlinear oscillators

A classical iteration procedure is applied to nonlinear oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. With the procedure, the analytical approximate frequency and the corresponding periodic solution, valid for small as well as large amplitudes of oscillation, can be obtained. Two examples are given to illustrate the accuracy and effectiveness of the method. Another advantage of this classical iteration approach is that it also works if the linear part of restoring force is zero.