re impulse response: absolutely. Try projecting out for 2 or 3 periods from the low prior to the event, and see how close you are. I have found that the average length of three adjacent waves is often 3x the normal period, as the lows readjust to the "natural" cycle.
"Now it occurs to me that perhaps natural frequency is always present but that an event causes a separate resonant cycle which runs at the same frequency and concurrently with the natural frequency up until the energy generated by the event has dissipated. Does this make sense?"
What you described can be demonstrated by the following chart, it is true.
Market Data 
Markets 
AI
