Right rear end shutter

Shutter in right rear.

I have a 2007 ford F150, purchased used. I noticed a slight virbration in the right rear tire/wheel area and it is there mostly at low speeds and more noticeable with a load on the truck, such as a trailer. I took it to Ford and there is a TB about this problem and they shimmed the rear axle at the shackles and it is still there. They had the vehicle several days and did not charge me, and said it was typical of that year of ford pickups. The truck has a 3:55 gear ratio and a slip differencial. I have not idea of what this could be and thought I would submit this to car talk.

Has anyone who has this year Ford F150 had this problem? Thanks for your reply

Try out this spot:

Have the two universal joints replaced. There are two in your truck. Labor and parts should be less that $100.

That would be one great deal to get that work done at that price,parts and labor. I would think more like $200.00

I had the truck into the dealer, why would they not have known this. I would gladly have the joints replaced if it will cure the problem.
I am still confused as it why all the symptoms show up in the right rear wheel area. If you have any additional input, feel free to submit your ideas.

labor is $100 an hour in my neck of the woods