When I first installed mine, I didn't mount the cradle right away. I just laid the cables in the back and stuck the crade and iPod inside the coiled cables so it wouldn't move around. It made the same whine that you descibed.

A few days later, I mounted the cradle and neatly rearranged the cable harness and the whine went away. I'm not sure if it was coincidence or if where the cables were sitting made a difference.