Application of Ultraspherical Polynomials to Nonlinear Forced Oscillations

Abstract

Approximate solutions to the conservative free-oscillation problem were obtained recently [1–4] through the use of ultraspherical polynomials. The present paper extends the technique to forced oscillations governed by ẍ + g(ẋ) + f(x) = F0 sin pt + F1 Very accurate results are obtained either by setting the ultraspherical polynomial index λ = 0 or, better yet, by restricting the choice of λ such that the solution to the forced problem is a perturbation from the nonlinear free oscillation solution. Examples are given.