Oscillator + Discriminator

Hello,

I've been given a variable area capacitor (C changes with displacement), and I need to measure the capacitance as I change it. I've also been given two circuits - an oscillator and discriminator. Apart from that I have no additional information. I do know that as the capacitance changes, the period of oscillation changes. The discriminator demodulates the signal to produce a dc output (I think).

I'm assuming I connect up the Cap to ext. comp. (right?), but how do I get some kind of expression for the output period at it relates to the capacitance?

Thanks