I really enjoy this channel: https://www.youtube.com/@WristwatchRevival He takes watches that need repair, disassembles them to basic components, washes them, and then reassembles and tunes them, replacing any parts that have broken (often the mainspring).

It doesn't have the explanations or the math, but the cameras are high quality and you can really see just how jiggly the balance wheel and spring are, and how the watch will just "spring to life" when you install those bits.

If you liked that video you'll like this one too, which explains that mechanical and electrical parallel but in the other direction.

Prof. Malcolm C. Smith had an electrical circuit and made its mechanical equivalent. His invention (the inerter) gave the F1's McLaren team an advantage in 2007.

https://www.youtube.com/watch?v=FhmLb2DhNYM

Valid link: https://videolectures.net/videos/mitworld_sussman_clock

For anyone with a sudden hankering for "what does that mechanical bit do", an interactive exhibit:

https://ciechanow.ski/mechanical-watch/

I remember watching MIT lectures in OpenCourseWare back in 2007, before I started at university. What an amazing resource it was at the time.

Sussman is a treasure. I love how deep he goes into topics.

Wrong TLS cert.

What a beautiful lecture