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
$x¨+g(x)˙+f(x)=F0sinpt+F1$
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.
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