Transfer Function of Potentiometer

[NHPhysics]

Hey guys, I am new to this forum.

I am working on a problem analyzing a potentiometer accelerometer. For the first part, I need to find the transfer function of the potentiometer.

known: y=x2-x1
dynamic system: y,x1

For the mechanical aspect of the problem, I found that the transfer function was --> Y(s)/(s^2)*X1(s) = -m/(ms^2 + bs + k)

For the electrical part, I know I need to find the transfer function E0(s)/Y(s) and multiply it with the mechanical part to form the total transfer function. I cannot figure out how to determine the transfer function though. I am assuming I should make 3 loops, where the e0 'arm' is moving along the resistor, but if I do this, i would have another loop with es as the input, would that come out to the right answer?

Actually, now that I'm more deeply thinking about it, the final transfer function for the potentiometer should be the input displacement of the circuit over the output voltage of the circuit right?

For loop equations I have:

R0*i1 + e0 + (R0 + R*y)*i1 = 0
R0*i2 + (R0 + R*y)*i2 +e0 = 0
R0*(i3 - i1) + R0(i3 + i2) + es = 0

Any help would be appreciated, Thanks in advance!

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?