Show that the elastic force of …

here exists a third category: force of constraint.

Forces of constraint aren't either conservative or non-conservative forces, because they never do work (positive or negative) of their own (only transmit work from other forces). I suppose if you had to classify a force of constraint, it would be conservative, since it doesn't cause any irreversible processes.

Forces of constraint either always act perpendicular to motion, or prevent motion in their direction.

Conservative forces will have an associated potential energy, such that when such a force does positive work on a body, the body changes from having potential energy to kinetic energy. The opposite occurs when a conservative force slows down said object.

Non-conservative forces are forces for which we aren't really interested in tracking associated energy, and even if we were interested it tracking said energy, processes involving non-conservative forces are irreversible, and it is useless to define an associated potential energy.