shollos

This is the credo of a physicist but I think most of it can be applied to almost any profession. A somewhat longer version appeared in Physics Today which you can find here https://pubs.aip.org/physicstoday/article-abstract/46/5/63/4...

Does anyone have anything to add to this?

I suspect an analog computer would work just as well for modeling coupled harmonic oscillators.

You can find C code for the Goertzel algorithm at: http://www.exstrom.com/journal/sigproc/index.html