Funny.
I find when my trailers (2 Cobras and a Solaire) starts to oscillate that a quick hard jab on the brakes stops all the bad motions. Doesn't make any difference whether the oscillations are started by an 18 wheeler passing me or by my increasing my speed too much. Acceleration just seems to amplify the swings.

I do find that making sure the trailer is very tongue heavy makes it stable and that tongue light makes it unpredictable.