We talked about forced spring vibrations. You can download a Sage worksheet that I used to generate the plots. Also, check out the disastrous consequences of resonance and the “beats” caused by amplitude modulation, both below.

(Note: for the sage worksheet to unpack properly, I had to use Stuffit Expander on a Mac. The build in archive utility didn’t work. You should get a .sws file after unzipping)

Resonance:

Beats:

Spring-mass systems (i.e. vibrations) bring this 90s gem to mind:

…And this older one: