The periodic property of Gaylord’s oscillator with a non-perturbative method

Abstract The Gaylord's oscillator is a vibrating of uniform rigid rod without slipping on circular surface with definite radius. dominant equation motion was the outcome strongly nonlinear pendulum second order. run article interested in obtaining frequency–amplitude and approximate solution by simpler approach. relationship derived terms Bessel function. Quasi-exact periodic depends non-perturbative validation analytical made through comparison numerical which shows excellent approval. Finally, method high accuracy besides simplicity if it compared other perturbative techniques analyzing behavior oscillators strong nonlinearities.