Ford: Rear Vibration, limited slip differential, ford f150 supercab

Question
Hi Dusty, I have a 2002 Ford F150 SuperCab. 4.6 engine auto transmission. rear wheel drive. I bought this truck used from a leased company and have had a rear end vibration for about 4 yrs. I try to ignore and then attempt to locate the culprit. The truck had 18,000 miles when I bought it. It now has 83,000. I just replaced the tires BFG Long Trail T/A Tour, this is the same as the original. Front end alignment and balanced at a local Ford Dealership. The only front end part that was replaced was the idler arm. Back to the vibration, It develops when the truck is acclerated to between 40 and 45mph, the seat and floor boards shakes. When vibrating I can put into neutral and it doesn't change the vibration until the truck slows below 40 mph. The steering is solid. The old tires were in excellent shape and were replaced due to age. The tires were the original tires. With the new tires the rear end vibration has actually slightly worsened. The vibration also is felt when accelerated to 55 and 80. There doens't seem to be any noise associated with the vibration. Recently after the new tires I had the driveshaft removed and balanced and a small weight was added. The shop foreman states the drive shaft didn't "act up". I also replaced the rear rotors and pads with Wagner brand rotor and pads. I didn't change with parking brake. They seem to be OK. They are not drapping on the drum of the rear rotors. The pinion is solid and the rear axles are tight with no fluid from the rear wheel seals. What can I do next to attempt to locate this issue on my own?

John

Answer
check your rear leaf springs for any cracks or wear and the u bolts. check the box and body mount bushings and bots, make sure they are all good and tight. although i doubt it is the problem, check your rear shocks along with the mounts, make sure there is no broken welds. if all good, pull the cover off the rear differential and check your carrier bearings. being 2WD i believe it is an LSD (limited Slip Differential) which has 2 traction locks inside the carrier, make sure nothing is loose, broken or can be moved by hand. jack the truck up, (after blocking the wheels) with the cover off and rotate the drive shaft (truck in neutral) and make sure everything turns smoothly. by the sound of it i think you have a Gremlin, a pesky problem that annoys the heck out of drivers and mechanics alike