1st run it without the collet & nut, if it still vibrates the spindle is probably bent and you'll need a new spindle!
2nd put a long steel dowel pin in a collet, if the pin wobbles the collet and nut could be bad!
I have seen collet nuts without the little holes drilled in them to balance them, they are the cheaper ones!
Cheaper collets are made so poorly, that the center bore is NOT concentric with it's outer diameters!