I feel almost ashamed to ask this - but I am mechanical engineer so hey

We are trying to calculate the resistance of a mechanical device (microcantilever).

We actually want to have the whole impedance model of the cantilever, but having

at least the resistance would be a good start.

Here is the problem. Following the circuit which I have attached, the cantilever

resistance would be given by:

Rc = (Vout/Vin - 1)*Rb

The tricky part is that we are supplying a voltage which has both AC and DC part,

therefore when carrying out that division a very strange curve appears for the

resistance ( [A*sin(wt) + B]/[C*sin(wt) +D] ).

Is it possible to just divide like we did, or should we separate AC and DC

calculations? The two approaches give out different results for the resistance

(one gives it as a constant - if we separate ac and dc calculations,

the other results in a quite strange curve as mentioned above).

I would say we should separate ac and dc, but something in my head also says to me that since

we have got only resistances in there ... dividing mixed ac and dc signals

should actually also work fine...

Btw, we expect to see a non-constant resistance in there, therefore I am not

happy with the solution we find by separating ac and dc, because if we separate,

and just look at the dc part, we have constants Vout and Vin, therefore constant

Rc.

Which one is the right path ?