Circuit/Mechanical oscillator analogy

[jdstokes]

Homework Statement

I've been pondering the analogy between an RLC circuit and a damped harmonic oscillator.

The inductor serves the role of the inertia, leading a finite charging frequency.

What happens if we remove the inductor, so that the system consists just of a charged capacitor, with each plate connected by a wire of resistance R?

The Attempt at a Solution

The mathematics suggests that the system will undergo oscillations with an effectively infinite frequency and that the amplitude will instantly decay to zero.

This doesn't seem to make sense. What would really happen?

 

[jdstokes]

For anyone interested, my initial guess is rubbish: with no inductor, there is no interchange between energy stored by the magnetic and electric fields, so the charged capacitor simply discharges exponentially to zero.