Larry --

Glad to help.  

>Karl,
>That would be a big help. What information would you need for the number
>crunching?

Off the top of my head, I think I would need the feedback circuit, the
characteristics of the feedback transducer (voice coil, or whatever), and
either the period or the amount of mass and the spring constant.  These may
not all be easy to come up with, but some relatively simple experiments can
be done to figure it out.

The calculations are very similar to what Sean-Thomas has posted on his web
site for the VBB, except for the circuit equations.

>Yes, but does the output at that point have a flat freq. response to
>acceleration above the period of the pendulum or does it fall of at the
>12db/octave or 6db/octave rate?

If the loop gain is high enough, the acceleration response should be flat
with repsect to frequency.  The idea is that if the loop gain is high, the
feedback will be maintaining the mass in a fixed position with respect to
the base (and the earth).  If this is the case, then the current in the
coil has to be proporational to acceleration (barring any friction in the
mechanical system), independent of frequency.  Of course, the response will
drop off at the extremes, but this will be predicted by loss of loop gain
at these frequencies.

Saying it another way, the loop gain also determines the measurement
accuracy, and for our purposes inaccuracy is approximately the inverse of
loop gain.  With a loop gain of 10, the inaccuracy will be within about 0.1
(10%).  I would think that determining acceleration amplitude within 10% is
probably good enough for us.

Loop gain in the center of the frequency range will probably be much higher
-- maybe 100 or more.

-- Karl


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