I have a 2005 Suburban That makes a nosie like mmmmmmm. It does. For about 3 seconds on acceleration only on the drivers side. So from stop to start I apply gas and right up by the drivers side I can hear a mmmmmmm sound for about 3 seconds. It sounds like the traction control, but that sound is just a little different from the one I hear from take take off postion. It happens about 4 to 5 times a day and I know that I'm not on a slippery surface.

Scott

 

Were you ever able to get this figured out? I have the exact same issue with my 05 suburban, only from acceleration.

 

I changed my motor mounts and noise was gone