RWD Transmission Output Shaft

[JonnyTahoe]

Removed the driveshaft from my 2000 Yukon yesterday I noticed the Output Shaft is loose. I could move the end of the splined portion of the shaft with very little effort about an eighth inch up down and side to side. I have had a vibration at about 1800 rpms for the past six months that's why I removed the driveshaft to replace the u-joints and have the shaft balanced. Should this amount be normal ?

 

[OR VietVet]

Best to hope @rockola1971 chimes in with his transmission expertise. The problem may be more than just that and he would know. I personally feel the vibes problem is likely that but if old enough, put the new u-joints in and balance the driveshaft as well.