Question about my 2003 ford mustang?

[Gene]

I have a 2003 ford mustang base model coupe v6 and automatic and wheel rear drive,I have been noticing in the morning when i come to a stop i can hear a loud rumble and feel a vibration in my car,its only there when i am stopped,and as the day goes on the rumble and vibration go away.I can feel the vibration in my seat and it feels like it may be my exhaust.What would cause the exhaust to do this,or does any1 know what it may be besides the exhaust