Recently, an approximate solution of the quadratic nonlinear oscillator has been presented based on the harmonic balance method. According to this method a set of nonlinear algebraic equations appear among the unknown coefficients of the several harmonic terms. Moreover, all these algebraic equations have no analytic solutions and sometimes no real solution can be found. In this article, a simple form of harmonic balance solution is obtained where algebraic complexity is partially reduced and all the related nonlinear algebraic equations are solved analytically.

中文翻译：

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求解二次非线性振荡器的解析技术

最近，基于谐波平衡法提出了二次非线性振荡器的近似解。根据这种方法，在几个谐波项的未知系数中出现了一组非线性代数方程。此外，所有这些代数方程式都没有解析解，有时找不到真正的解。在本文中，获得了一种简单形式的谐波平衡解决方案，其中，代数复杂度得以部分降低，并且所有相关的非线性代数方程都可以通过解析求解。