I was thinking about this last night and the following occurred to me. I've often noticed that a given cycle will be running regularly at whatever rhythm (let's say 14 bars), then there will be an event which will cause a non cyclical low at say bar 4. This will often lead to a confused situation in which it is no longer possible to clearly identify the cycle low of the 14 bar cycle or those of a lesser dimension for a period of time.
Often in this situation I will find myself "seeing" both lows which fit the original cycles and lows which fit cycles re-set to start form the low caused by the event. Thus I'm unable to be sure where the "real" cycle is anymore.
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.