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Mathematical Problems in Engineering
Volume 2012, Article ID 618750, 12 pages
Research Article

Approximate Solution for the Duffing-Harmonic Oscillator by the Enhanced Cubication Method

Departamento de Ingeniería Mecànica, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico

Received 15 April 2012; Revised 1 July 2012; Accepted 23 July 2012

Academic Editor: Rafael Martinez-Guerra

Copyright © 2012 Alex Elías-Zúñiga 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.


The cubication and the equivalent nonlinearization methods are used to replace the original Duffing-harmonic oscillator by an approximate Duffing equation in which the coefficients for the linear and cubic terms depend on the initial oscillation amplitude. It is shown that this procedure leads to angular frequency values with a maximum relative error of 0.055%. This value is 21% lower than the relative errors attained by previously developed approximate solutions.