More coffee cup physics (or, am I quite sane?)

So last Friday, after a hard week at the office, I went over to the Opus Bar on campus to enjoy some evening music.  And, because I wished to consume neither alcohol (I had to drive home) nor caffeine (I didn’t want to stay up till midnight), I bought a hot chocolate.

This came with two marshmallows.  I plonked one of them into the hot chocolate, and it landed right in the middle, where it stayed slowly began to sink through the foam.  Wishing to encourage it, I gave it a poke with a spoon, and then noticed the very uniform, circular ripples that ran from the centre to the edge of the cup as I poked it.  Being the physicist that I am, I started poking it at a resonant frequency, so that the ripples built up into a clear oscillating pattern.

Is this behaviour normal? Do I need therapy?  I mean, does a sociologist walk into a cafe and immediately start noting the ethnic make up of its customers, or does a mathematician start looking at the cappucino:flat white price ratio to determine the best buy?

For the record the shape that is generated (see animation – in my case I think I got the 0,2 mode) is described by a what is known as a Bessel function; which crop up everywhere where there are waves on things with circular symmetry, but you really didn’t want to know that, did you?

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