Floating Rear Rotors?, Making noises Options

[ILoveMySilly97]

So I recently installed extended lug studs and in the process I had to remove the rear rotor. Before I did the work. The rotors were fine. It didn't move side to side. But once I took it off and put it back on. Both sides can move side to side. Like if you put it up on jacks and take off the wheel. You move the hub assembly by moving the studs. The studs will hit the rotor. I know before the studs would just stay still along with the rotor. I'm not 100% sure this is what's making the noise but I'm Pretty sure it is what's making the noise. I did install the Rotors properly with them lil spring thingy for the horse shoe inside. Don't know what it's called. Any suggestions? The noise sound is a clunk sounds like something hitting against eachother. It's not screeching and you can hear it once I go like 10mph and up. The faster I go. The faster the clunk is. I know it's no the suspension either because it happens on a smooth paved road also.