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On my '11 5.0L I've noticed at light to mid throttle if I get into 5 or 6 with the rpms down near 1k or so it will have a light but noticeable to me shudder type sensation. At first I thought maybe it was a converter lockup effect or possibly road noise but the more I drive the more I notice it. Very indistinct and mild with no check engine light and mileage was 17mpg mixed so I'm pretty convinced its not an engine shutter- but I have no experiencing dealing with these coyotes yet...
You are probably just (for lack of a better term) lugging the engine. It is a high amount of load on a slow turning engine that will cause that shudder. To verify it, try manually dropping the transmission down a gear when it happens. That should help smooth out the engine.
Yup, sounds like you're lugging it a little. Modern transmissions like to hold as tall of gear as possible and keep the torque converter locked for as long as possible, both to help with fuel economy. That means you can sometimes get it to lug a little, just like a manual transmission in too tall of gear.
If you put the truck in manual mode, select a gear, and then get the RPMs down as low as possible, see if it will do it. Try it in various different gears with various amounts of throttle input.
Also, see if it will do it in Tow/Haul mode. I know tow/haul tend to be a bit more aggressive with the upshift/downshift timings.
If you mess around with it enough you might be able to tell if it's just lugging, or if it's another issue.
One thing you could try is disconnecting the battery for about 20 minutes. This will cause the transmission's adaptive memory to reset, at which point it will go through a relearn procedure. It will shift funny for a little while, but as you drive it, it will learn new parameters and possibly adjust itself to the truck, and your driving style, more appropriately.
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