Can anyone help me with what I think is a nose wheel balance issue? Lately I've noticed about 30 seconds after takeoff a vibration that lasts for a few seconds and dies out. I usually tap my brakes just after lifting off to stop the mains from spinning, so I am pretty sure it is the nose wheel winding down. Also, occasionally when the nose wheel comes down it will shimmy. Some times it's pretty strong. Anyone got any advice? What do I look for - bearings, balance, what?

Thanks!