Intermittant vibration

I was unsure whether to post this in the transmission section or the suspension section as I'm perplexed as to where the problem is coming from. 95% of the time, the car (2.8 FL) drives perfectly well, then for some reason the car starts to vibrate. After slowing to around 55mph and driving a further 2-3 miles, the vibration dissapears and might not reoccur for weeks. I "think" I can get it to start the vibration by acceleration hard in "S" mode from a standing/slow start, but this isn't 100% repeatable.
Anyone got any ideas what the cause could be?