Author(s)

Serge Bruno Yamgoué¹, Bonaventure Nana¹, Olivier Tiokeng Lekeufack²

¹Department of Physics, Higher Teacher Training College-Bambili, The University of Bamenda, Bamenda, Cameroon.
²Laboratory of Mechanics, Department of Physics, Faculty of Science, The University of Yaoundé 1, Yaoundé, Cameroon.

We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.

Harmonic Balance, Linearization, Continuous Force Function, Single Degree-of-Freedom, Conservative System, Jacobian Elliptic Functions, Symmetric Oscillations

Yamgoué, S. , Nana, B. and Lekeufack, O. (2015) Improvement of Harmonic Balance Using Jacobian Elliptic Functions. Journal of Applied Mathematics and Physics, 3, 680-690. doi: 10.4236/jamp.2015.36081.