I have 06 f150 4wd with 115k miles. Have a pulsing vibration that has gotten bad. Happens from 0 to 15 mph on acceleration and only occurs after truck has been driven 30 min or more. It is barely noticeable if driven around town. Ford mechanic said torque converter going out and I did have some transmission ware so I had the whole thing replaced. Didn't help. I have searched similar threads but their problems differ slightly, most others problem happens at any or higher speed whereas mine doesn't. Me and a local mechanic searched it but could locate issue. Anyone know what's up?

 

A bad universal joint can vibrate at different speeds. Also a new exhaust system can vibrate if there is to much tension on it when installed. I have seen them have to be loosened and retighted before a vibration disappeared. Some Lincoln Town cars had this problem right off the assembly line.

 

Had a similar problem with my '06 4x4.

I took off for work last week and I heard a VERY faint vibration/dragging sound and felt the vibe. I turned the radio off and rolled the windows down and was able to tell it was in the back. It almost felt like I had a bald spot on my tire, as it was once every revolution of the tire and sped up with vehicle speed.

I immediately pulled off the road and inspected my tires, which were fine. Then I noticed that my left output seal had some seepage and my rear diff was leaking. I let it sit for the day and it leaked enough to make a puddle the size of a dollar bill folded in half.

Took it to my mechanic and he took the rear diff apart to find that the pinion and spider gears had briefly seized and broke loose, and were showing signs of heat damage.

I'm currently waiting for Monday when he'll be able to get a parts quote.
On Friday he quoted $320 for the rear diff seal, fluid change, and left output seal, but that was before he took it apart and found the other stuff.

Hope that helps.