Jib car location was discussed in several threads recently. It has to do with sail twist. If you seem to be getting luffing first near the head, move the car forward (this will pull the clew down, and tighten the leech). In lighter winds when you want more bagginess, move the card aft.
A general guide is that the sheet should be more or less aligned with an imaginary line from the middle of the luff to the clew.
Everything being equal if you are getting oscillations on only one tack, a wild guess would be that your shrouds may need to be tuned up.
1978 Gulfstar 50'
Clark Sailing Dinghy 10'