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Mathematical Problems in Engineering
Volume 2013, Article ID 670845, 11 pages
Research Article

Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey E. Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico

Received 20 May 2013; Accepted 5 September 2013

Academic Editor: Hossein Jafari

Copyright © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero. 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.


The aim of this paper focuses on applying a nonlinearization method to transform forced, damped nonlinear equations of motion of oscillatory systems into the well-known forced, damped Duffing equation. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the amplitude-time, the phase portraits, and the continuous wavelet transform diagrams of the cubic-quintic Duffing equation, the generalized pendulum equation, the power-form elastic term oscillator, the Duffing equation with linear and cubic damped terms, and the pendulum equation with a cubic damped term.