First off jack the car up. Attempt to turn the DS by hand. If it has excessive movement ensure that your pinion moves right with it and doesn't have ANY slop in it. If it does replace that ujoint IMMEDIATELY. Also inspect the front unjoint and ensure that the tranny yolk moves right with the driveshaft. Again ANY slop replace that ujoint IMMEDIATELY. A ujoint coming apart can tear up the car badly if it drops the driveshaft. A friend of mine with a LT1 swapped S10 had this happen and the DS knocked a hole in his gastank

Other considerations here. Could be the output bushing in the tranny is shot. Could also be like others said the ring and pinion backlash is outta spec. Too many things to look at just on the internet. I would start with the DS though being that is usually where all the problems originate from. Good luck. If you do replace the ujoints then you have alittle bit of work ahead of you if you have never done it before. Basically you need a torch, a hammer, and a old socket about the size of the bearing cap on the ujoint if you want to do it the brute way

Basically you have to heat right by that bearing cap on the DS and on the yolk because GM uses a liquid nylon lock on the factory ujoints and they won't come out unless you heat the thing really really good. Basically you will see a little tit on the yolk and DS where there is a small amount of the nylon left from when they injected it. Heat those caps until you see the nylon ooz out of there. Hope this helps if you have to replace the ujoints.