I have my car for about 1 week now it’s a GT I put 350 miles on it. Every morning when I start the car I feel the car shaking until it worms up and also sometimes when I am sitting and the car is idling I feel it also. I wanted to know if that's normal before the engine is broken in and if anyone else is experiencing the same thing.

Yes many are experiencing the same thing. There is a topic on that in the forums already

http://www.g8board.com/forums/showthread.php?t=1759