2000 Civic EX 4 Dr. AT @75K miles.

I have recently purchased this vehicle and the only real work I have done is had the timing belt replaced.

I do however have a wierd vibration/grinding noise that gives me some concern.

It only occurs after you put the car in gear and you are moving. It happens in reverse as well as drive and it happens after about 15-20 feet of moving.

It vibrates/grinds for about 2-5 seconds and stops. It does not do it again (or at least I do not feel or hear it) until you start the car again and begin to travel. It does it without fail each time I start to travel.

Any ideas?

Thanks for any help sent my way!