I'd like to find an approximate relationship between the peak velocity for an aerogel resonator, resonating at (angular) frequency $\omega$, and the amplitude of motion.
Essentially the fact it's aerogel is irrelevant; I need the relationship between peak velocity and amplitude of motion for an object driven by AC current in a magnetic field.
I am doing an experiment which will involve calculating the normal fluid fraction using such a resonator. I assume it in some way involves the relations $F = IlB\sin(\theta)$ and $\epsilon = Blv$, but I can't think how to derive the required relationship from there.
The resonator will be glued to a wire shaped like a rectangle but with the base missing. The vertical sides, which are the shorter sides of the rectangle, are $5mm$ apart so essentially then $l = 5mm$. It'll be driven by AC current $I = I_0 sin(I\omega t)$, haven't quite decided at what frequency exactly. Any help is much appreciated!