A nonlinear oscillator describing dynamics of parallel plate capacitor is considered with zero initial conditions. This case of initial conditions makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, inapplicable. To overcome the shortcoming of classical methods, a simple transform is proposed to convert the problem into a traditional case where a standard frequency formulation is used to obtain the approximate solution. Microelectromechanical system (MEMS) oscillator is used as example to show the solution process. The obtained results are illustrated and compared with high-precision numerical solutions.

中文翻译：

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振荡平行板电容器微机电系统模型周期解的简单近似

以零初始条件考虑描述平行板电容器动力学的非线性振荡器。这种初始条件的情况使得一些行之有效的方法，例如变分迭代法和同伦摄动法，变得不适用。为了克服经典方法的缺点，提出了一种简单的变换，将问题转换为使用标准频率公式获得近似解的传统情况。以微机电系统 (MEMS) 振荡器为例说明求解过程。得到的结果被说明并与高精度数值解进行比较。