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Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

Published online by Cambridge University Press:  03 June 2015

Malik Mamode
Malik Mamode*
Affiliation:
Department of Physics, Laboratoire PIMENT, Equipe MASC, University of La Réunion, 97400 Saint-Denis, France
*
*Corresponding author. Email: malik.mamode@univ-reunion.fr
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Abstract

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

Keywords

34A3434C1534C25Nonlinear oscillatorexact periodelliptic integral
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 6 , December 2011 , pp. 689 - 701
Copyright
Copyright © Global-Science Press 2011

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