Dont know of SAR Heli's - but if a Chinook (C/D model) had a load resonance issue then it used to be recommended that the driver/jockey was to let go of the cyclic controls and let the Auto Stabs take over.
That eliminated human influences (trembles?) getting into the flt control system and was supposed to settle the resonance within 1.5 to two 30-to-45-degree swings.
That was for the three load hooks mounted in the Centreline of the beast directly influencing attitude(s) somewhat. Don't know if this would work on an external Rescue Hoist.
I remember seeing a Chinook Load Test film of such an event but can't remember if it was a Boeing or a UK JATE film.
Rigga