My 2008 F150 has develed a vibration when starting from a dead stop. It doesn't occur each start, but does seem worse when the vehicle is cold. I can't narrow it down but it feels as if it is coming form the rear end or drive train.

 

Is it a quick clunk? Or a rumbling feeling?
Have you checked the balance on your tires? Could be a U-joint going out.

 

I'd check the u joints first.

 

I would best describe it as a rumbling feeling, not jerky.

 

Maybe your parking brake lever is seized up. That was what my intermittent rear-end shuddering ended up being. Here is a video showing the part. Step 2 is the part that frequently seizes up.

 

Tail shaft pilot bearing ? AKA pinion