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The purpose of this paper is to present an analytical approximate technique to solve nonlinear conservative oscillator based on the He’s energy balance method (improved version recently presented by Khan and Mirzabeigy). The method is illustrated by solving double well Duffing oscillator.

The Duffing equation with a double-well potential (with a negative linear stiffness) is an important model of a mass particle moving in a symmetric double well potential. This form of the equation also appears in the transverse vibrations of a beam when the transverse and longitudinal deflections are coupled (Thompsen, 2003).

The approximate solutions obtained by the present technique have good agreement with the numerical solution and also provide better results than other existing methods.

The results are more accurate than those obtained by other existing methods. The relative errors obtained by the present paper are less than those obtained by other existing methods. Therefore, the present technique is very effective and convenient for solving nonlinear conservative oscillator.

The purpose of this paper is to present an analytical technique, based on the He’s energy balance method (an improved version recently presented by Khan et al.), to obtain the approximate solution of quadratic nonlinear oscillator (QNO).

This oscillator (QNO) is used as a mathematical model of the human eardrum oscillation.

It has been shown that the results by the present technique are very close to the numerical solution.

The results obtained in this paper are compared with those obtained by Hu (harmonic balance method) and Khan et al. The result shows that the method is more accurate and effective than harmonic balance as well as improved energy balance methods.