Did not welcome you to the site, so welcome:
You bring a common question to the boards, and the answer is as simple as can be.
You F-150 is equiped with a limited slip rear differential, and you are feeling the clutches chattering. This can feel a little funny around corners, especially under a decent amount of acceleration.
This is telling you that either the rear diff is low on fluid, or that it is need of service. It could also tell you that it has been serviced, and there was simply not enough "friction modifier" installed, or maybe none at all.
After you can determine that the proper fluid and level is in the rear end, you simply add a bottle of friction modifier to the diff. This is available from your local ford dealership, and will fix that little chatter right up.
If your level is low, you will then have to figure out where the leak is, and fix that. Pinion seals often leak, but the vent can get plugged too, and pressure will build, thus pushing fluid out.
Find and repair any leaks.
No problems, just verify your fluid levels, and it is as easy as pie to add a little bottle. You will impress yourself with a job well done!