Picking up clips = transient domain; holding many clips = steady-state domain.
Short circuiting an ideal capacitor gives you infinite current for zero time with the area under the spike "curve" <> [not equal to] 0; definitely transient domain.
Discharging a cap with low ESR into a low resistance gives you a current spike over and above what the battery is delivering; definitely transient domain.
Discharging a cap with low ESR into a low resistance in series with an inductance gives you something I'd have calculate.
If this series RLC circuit is underdamped (Q factor > 1?) you'd get a decaying sinusoidal current waveform (which I don't know if that would help or not). Overdamped, you'd get a big decaying current spike, probably modeled in the time domain by the sum of two e^x terms.
You'd hook the cap to the battery first, then switch on the coil.
I'll have to get back to you on this; I haven't done Laplace domain stuff for decades.
We're definitely having fun, now.
It would be good, after all this effort, if you actually won.