  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 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 quantum field theory
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.
