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Shock and Vibration
Volume 2014, Article ID 624147, 8 pages
http://dx.doi.org/10.1155/2014/624147
Research Article

Parameters Approach Applied on Nonlinear Oscillators

Department of Mathematical Sciences, University of Karachi, Karachi 75270, Pakistan

Received 8 August 2012; Accepted 12 May 2013; Published 13 March 2014

Academic Editor: Didier Rémond

Copyright © 2014 Najeeb Alam Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection . This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of , the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.