07 Silverado Classic shaking during acceleration

I've got a 2007 Silverado Classic crew cab with the 5.3 V8. When I accelerate hard, I feel shaking, like the engine on its mounts or something. It doesn't make any funny noises and is doesn't hesitate at all. Anyone ever experienced this?

The dang brakes also don't seem to release sometimes and sounds like it is making ABS noises after I've slowed and turned a corner from highway speeds.

The Chevrolet shop can't find anything wrong with it. The truck is all stock except for a K&N air filter. It has about 5,000 on it.

it's under warranty; take it to the dealer.

I have a Duramax and it does this when I'm towing a trailer and under hard acceleration from a stop. It quits at about 20 mph and I was told it was called "Launch Shudder" caused by a 2 piece drive shaft. They said I could try switching to a 1 piece drive shaft, but I chose to just live with it, it's been that way since the truck was new and it now has 75k on it. Don't know about your '07 but it may be something in the drive line.