In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of more than one oscillator to see how the frequencies of small oscillations change when non-linear terms are added to a linear system and observe an interesting beat phenomenon in degenerate coupled oscillatory systems.

在存在相互作用的情况下，简谐振子的频率偏离非相互作用的频率。可以使用各种方法来计算频率的微扰变化。其中一些类似于量子场论 (QFT) 中使用的方法，其中在添加相互作用时运行理论参数的裸值。在本文中，我们回顾了其中一些技术，并介绍了一些符合 QFT 方法的新技术。此外，我们研究了多个振荡器的情况，以了解当非线性项添加到线性系统时小振荡的频率如何变化，并观察简并耦合振荡系统中的一个有趣的节拍现象。