@_thegeoff who specifically might find it interesting
Consider a pot with a convex bottom (i.e. it will stand on its midpoint) with sufficiently large radius of curvature to make it stable when filled to any level. When you put such a pot on an electric hotplate and get it boiling, it starts rocking: https://www.youtube.com/watch?v=vB_szsLa3zk
I have a hypothesis on what's going on (the pot rocks away from the area where the boiling is more intense due to density difference, contact with hotplate increases rate of heating, so there's more heating on the side that's currently lower and thus any rocking gets amplified). Sadly, I don't have the pot anymore and didn't thing at that time of any experiments that could falsify this hypothesis.
@robryk (1/2) Lovely! My hypothesis here is something most people don't realise about boiling water with a hot surface:
Turn on an electric kettle. It starts to make noise as the water gets hotter, and gets louder the hotter it gets, but then just before it boils it gets quieter again.
Seriously, I made a graph a few years ago.
@robryk The critical thing is what makes the sound: it's not bubbles going pop (well, it is at the very beginning as the water expels dissolved gas), it's bubbles of gaseous water...not "steam" as in stuff in your bathroom, or mist, but actual gaseous H2O.
This forms close to the hot surface, a pocket of it starts to rise. But it quickly hits cooler water and condenses, and that happens *fast*!
The collapse is violent, a little hammer blow. It's what makes the noise, and maybe moves the pan?
That is a reasonable alternative hypothesis (that we basically get white-ish noise that pushes a dampened pendulum around, so the pendulum will end up with some amplitude of resonant oscillations). It should be easily verifiable if I had such a pot (basically insert a membraneless speaker with the axis oriented radially, play white noise, and see what happens). Perhaps I should find an old pot and reshape it that way with some wood and a hammer.
I realized that I'm actually not sure how a harmonic oscillator driven by noise from e.g. a Wiener process (but without damping) should behave (would its amplitude diverge? probably not).
