Rattle noise only when car is moving and in gear

My car rattles only when it is moving and I take my foot off the gas at around
30 mph. It does go away after running it for about 15 minutes. I have had the
exhaust system checked. No problems. The sound is like a cross between and
rattle and vibration and is a fast sounding noise. While driving, I take the car
out of gear and rev the engine. No noise.