Hi and welcome @joshu3a !
There is certainly a way to model this, though I am (unfortunately) too far from the basic physics of oscillators to spin up the code.
Generally, if it is just about regression, the following example used to help me personally:
https://docs.pymc.io/en/v3/pymc-examples/examples/generalized_linear_models/GLM-robust.html
… unfortunately it is not up to date. But there might be other useful traces in the v4 examples.
Generally, I find probabilistic models very useful to estimate parameters underlying noisy data, in very simple models. I have a simple measurement documented here, but that was also quite a long time ago 
Hope this helps!