Questions about 4x4 engagement

[carlos127a]

I recently noticed that my k1500 shakes the front right tire when in 4x4. Ive probably had that shake since i bought it but i never noticed it on ruff terrian .im assuming its the half shaft .when in 4x4 it takes a good minute until it disengages would that be the encoder motor, front axle acutuater etc?

 

[carlos127a]

Update i went under the truck and grabbed the suspected worn axle and it seems like the play comes from where the axle bolts on to the big diff case

 

[MIHELA]

At that point its usually easier to swap in a new diff. We just saw an 05 Yukon last week that did that. The axle stub would move about 1/4 inch, and it would clunk each time it went around in gear in the air.