"Resonating at DC" is a meaningless statement; or, perhaps even better: okay, fine, sure, whatever -- but at DC, you have zero power transfer, so, so what?
Time domain and pulsed analyses inevitably fail on this sort of thing. In my first real job, I was tasked by the company president to design the "fastest possible control" for induction heating. He thought it could be done every 1/4 cycle. What's so special about 1/4, versus other fractions of a cycle, I don't quite get, but he clearly didn't get the continuity of a resonant circuit: its behavior depends on a long history of past inputs, namely, the last (Q / f_0) seconds, give or take. (It's a weighted average over time, tapering off exponentially towards zero with that time constant. There are no hard cutoffs in this kind of system.)
I eventually convinced him to be satisfied with the system I designed, a digital PID controlled PLL, updated each cycle, with a one-cycle pipeline (so, the timing for the next power cycle is calculated during one cycle, using the sampled measurements from the previous cycle). That made the RMS calculations tricky (measuring output V/I/P) since the average was done over a variable number of ADC samples (typically a few hundred).
That was still quite a bit excessive, as the PID constants we chose ended up quite small.
Anyway, even with perfect tuning (a frequency-agile induction heater is a rather special case, as it has to sweep to find its operating point, which isn't usually at resonance anyway, but another set limit instead), you're limited on startup time because of the Q factor.
Another way to put it: you're storing so-and-so much resonant energy, but only delivering (or extracting) so much every cycle.
Note that Vrms*Irms == VA, but if it's all VARs, this has units of energy -- in the same way that torque (N*m) is a unit of force, a "sideways" (rotating) force.
Tim