Why doesn't a capacitor behave like a swinging pendulum when discharging? Please note that I'm not asking about solving the differential equation, but rather about how we are constructing it. I have a physical intuition about how things move towards equilibrium, like pendulums or a vibrating membrane (which I've seen as a model of a capacitor), and the solution for the capacitor is different.
When a capacitor discharges in a RC circuit, it reaches a voltage difference of 0 asymptotically. I understand that this is predicted from the differential equation:
0 + Q/C + dQ/dt = 0
dQ/dt = -Q/RC
I understand the approach of writing the equation by accounting for voltage drops around a loop. I understand that the solution to this equation is an exponential, and how to find the solution.
What I don't fully understand is why the voltage drop across the resistor is modeled using Ohm's Law as -RI or R dQ/dt. I know that Ohm's law is used to relate the voltage drop and current across the resistor, and I am comfortable with its use in situations where current is not changing. But here the current is changing, and I'm not certain that that the statistical justifications of Ohm's law that I've seen acknowledge the possibility of time-varying voltage or current.
What I'm wondering about is whether the moving charges have inertia that allow them to partially charge the capacitor in the reverse polarization. I asked a related question some time ago about AC circuits, but I feel that this scenario is actually simpler to describe. To that other question, someone referenced parasitic inductance as affecting the oscillation. I want to ask about this system of an RC capacitor to get at the issue of whether there are regimes (high voltage or current?) where the capacitor ever overshoots past 0 volts to reverse polarization.
The two possible scenarios that I see are: a) it never reverse polarization and does truly reach 0 asymptotically b) there is an acquired kinetic energy or inertia or parasitic inductance or some other reason why the capacitor overshoots and it oscillates asymptotically to 0 volts