Perturbation Theory for Damped Nonlinear Oscillations

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Abstract
A perturbation theory has been worked out for the decay of autonomous, nonlinear oscillations in the case where there is large linear damping. The solution reduces to a solution obtained by Kryloff and Bogoliuboff for small damping and to the perturbation solution for periodic oscillations for vanishing damping. The solution is applied to the decay of oscillations in Duffing's equation. In this case it shows good agreement with a solution obtained by numerical integration.

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