Modal analysis for a spring connecting two disks

If you need to do free-free modal analysis, just choose unconstrained and rigid mode search.  The first 6 modes will report very low frequency rigid modes, then the 7th and above will be the free mode shapes for the system. The general spring idealization used here would need properties that are based on the real spring and likely the Y and Z stiffness is different than the X stiffness. Of course I am assuming X is along the main axis of the spring. There is an icon on the end of the spring icon that shows the Y and z directions for the spring. There are some literature/formulae for determining Y and Z stiffness of a spring within the initial linear range and assuming coils never touch each other. (search: coil spring bending stiffness) Otherwise you could model the spring and simulate its full 3D stiffness. If you need help creating a 3D model of a spring, I think that is a separate question from the perfect answer provided by @skunks