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I also have a 5.4L vibration problem. I've been to the dealership twice and been told it was normal. Yeah, right. I have a 99 4X4 F-150, and it does it only when stopped and in drive with my foot on the brake.
It looks like this post is quite old, but I have the same problem.
I have a 99 F150 4X4 5.4L and I have had this into the dealer quite a few times. First they told me it was a problem with the Octane I was using. then they told me it was a "Harmonics Issue" and there was nothing they could do. Then they finally told me it was just like all the other F150's on the lot, and I should not worry about it.
I have a 1998 F-150 X-cab with a 5.4 and it always had a slight vibration in it since day 1 I bought it . The tech's say sometimes it's the computer trying to compensate for the different air to fuel ratios at different temperatures. I say that's bull!!!!. My uncle who has been a Ford mechanic for about 20 plus years keeps telling me I'm putting to much oil in the motor and that's what's causing the problem. the owners manual says 6 qts. but it doesn't registers full on my stick. I usually put 7 qts. in it but when I put 6qts. the vibration went away at idle.
I have about 60,000 miles on my 99 5.4 4X4 and have had no problems as of the present with the vibration getting worse or damaging anything. I use Mobil 1 and I just noticed it started actually burning oil the past 2 oil changes. It still runs strong and smooth.
I also souped up a 2000 Expedition for a customer and noticed that after the mods (the same ones as on my truck), I noticed a slight vibration that wasn't present before. My guess (and that's all it is) is that the computer is somehow affected slightly with all of the different parameters that have changed.