I have a G35 Coupe w/5at that under specific circumstances makes the car shake badly. If im using little throttle, like barely touching the gas pedal, when going up a hill around 35-40 and the torque converter is locked I will let it deaccelerate a little bit, to about 30-32 where it would downshift from 5th to 4th. And if the TC is locked and that happens the car begins to shake/vibrate violently. It has happened a couple times, and I can feel it in the gas pedal, steering wheel, through the seat, and through the shifter.

But, I notice if i give it enough gas while it's shaking to unlock the TC and have it rev up a bit, the shaking stops.

It only shakes in that circumstance. Accelerating through 4-5 normally, slowing down coasting, slowing down little throttle on no incline does not make it shake. Only shakes up a hill from 32-34mph or so in 5th.