Electro-mechanical oscillator confuses me

[ante_S.]

Hello, everybody!
I got a homework that confuses me totally. Any help is highly appreciated:

Here's the scenario :
http://cafeking.2page.de

Which frequencies are possible on the assumption that we have a harmonic oscillation?
The changing of the charge on the upper plate by q and the momentary elongation x should be considered.

I think 'harmonic oscillation' means that we have
x=xmax*sin(omega*t)
and its derivations as a solution for a differential equation but I can't find an accurate

the springs are made of isulating material.
I forgot to mention that we have a DC voltage, so the resistance of the capacitor is infinite. In contrast to a AC voltage it has no impendance. As a consequence of that we have a mechanical oscillation - not an electric one.
It must look like this:
m*s'' + k*s = E*q

The electric field strengh E and the carge q must be replced by given parameters whereas the charge on the upper plate is influenced by the coil - especially because of self-induction that hampers the charging on the plate.
That's all I can say. My problem is the right equation for the oscillation.

 

[lightgrav]

well, the natural frequency of oscillation doesn't depend on the driver.

But even after the capacitor is fully charged, to the DC Voltage,
the Energy stored in the inductor's B-feld will continue I flow.
After Voltage overshoots V_DC , oscillation w~ sqrt(LC) damps to V_DC.

Presume small oscillations, and small separation, so Q_bottom = - Q_top.