Sustaining amp circuit for MEMS oscillator
Try this although I'm a bit out of my depth: -



The mems resonator above looks like a double cantilever to me and it appears that input to and output from are via capacitive coupling (see drive electrode and sense electrode). The dimension of 50um is on one of the cantilevers and, I imagine that it's movement creates a twisting effect on the sense electrode thus altering capacitance and generating a sense signal when polarized with DC.

Here is a useful document (entitled CMOS Micromechanical Resonator Oscillator) that importantly has this diagram that kind of puts into perspective what I said above: -



It also contains the picture below that gives a detailed interface circuit: -




  What is a simple circuit that will achieve this? I need a circuit that
  will drive the oscillator at its resonant frequency. I need the
  simplest circuit possible, just for mathematical modelling purposes,
  so I'm not interested in advanced features or practical
  considerations.


Ah, if only everything in life were simple but maybe the circuit in this document (entitled Drive Amplitude Dependence of Micromechanical
Resonator Series Motional Resistance) will help: -



There are a few other documents listed here