Ford F-150 (2009-2014) :: 2012 - Shudder And Thunk While Accelerating?

In june of 2014 I purchased a 2012 F150 Harley Edition with the 6.2 for my wife to use as a daily driver. I told her that she could have any vehicle she wanted and she chose the White Harley Truck.

It is a Ford Certified Pre Owned and we took delivery with about 30,000 miles on the odometer.

From the test drive in June 2014 until today the truck has had two distinct issues with the rear end and suspension:

1. After coming to a normal stop (at a light) when you start to accelerate (on green) there is a distinct thunk that is heard and felt. Having owned other vehicles with a slip yoke drive shaft I knew right away that the slip yoke needed to be cleaned and lubricated and that is how the dealer repaired this issue. The repair lasted about 10,000 miles and the thunk started again recently.

2. Also after coming to a normal stop and then accelerating there is a vibration felt until the mass of the truck is moving along at about 20 MPH. It's not a vibration like a wheel/tire is out of balance it's more like the whole vehicle is shaking similar to the Space Shuttle Experience ride at the Kennedy Space Center. The shudder is severe enough that my elderly neighbors asked if the truck "was going to make it without falling apart" when my wife and I took them to dinner one evening. The Shudder is exponentially worse when towing any kind of trailer. I have a tandem axle car hauler to haul a 1992 Jeep YJ to various events and the whole setup might weigh 5000 LBS max which is well under the tow capacity of the truck. To say the shaking is violent is putting it lightly.

When I took it in for service, the dealer told me that it was my fault for riding around with the locking differential locked. I told them nice try and that I know what a locking diff is and how to use it because I have two of them in my Jeep. I then took the service advisor for a ride, made him verify the diff is off and demonstrated the problem without even leaving the parking lot. At that point he acknowledged the condition I left the vehicle with him again. The repair the dealer made was to change the rear differential fluid and called me to say the truck was ready.

I drove back to the dealer again (35 minutes in light traffic) where I was presented with the vehicle. I didn't have to leave the lot before I knew it still was not fixed and pulled back into the service lane. I was greeted by the advisor who then proceeded to tell me it was "characteristic of the vehicle." I was completely frustrated and took my truck with it's "characteristic" shudder home.