First, always give the specs on the truck, helps eliminate confusion.
For instance, the suggestion I am about to give might not pertain to your truck.
If you have a slip joint in the rear driveshaft, try greasing it. They can bind up and give that kind of effect.
Also, check the u-bolts that hold your rear axle on the springs and the spring hangers.
For the U-joints, chock the wheels, put the truck in neutral, and get under and wiggle the shaft. Twist it back and forth, up/down/sideways. You are looking for slop in the u-joints.
Also, if you see the little cap in the joint has been spinning, its bad.