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!

  • $\begingroup$ Don't think that many people even know what an "aerogel resonator" is. I had to google it myself. If your question is something that can be answered by someone who is not a specialist in low-temperature experimental physics, then it would be helpful to better describe the problem and include a figure. $\endgroup$ – Samuel Weir Feb 3 '17 at 6:40
  • $\begingroup$ @SamuelWeir Ok good point. I think the fact the resonator is aerogel is actually more or less irrelevant; the same relationship will hold as for any object resonating at angular frequency $\omega$. $\endgroup$ – user13948 Feb 3 '17 at 8:18

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