Initially , the current through the spring is 0.It is then increased to reach a constant value.Thus the magnetic fileld due to each loop increases from zero to a constant value.So, there will be a force acting among each loop of the spring as each loop acts as a magnetic dipole.But when the spring reaches the position where the magnetic force and the spring force are in equilibrium, the spring will have gained some velocity.Thus it will get compressed a little further before coming to rest and will thus osscillate about the equilibrium position.

 

I think this should be how it goes.If I have made some mistake pls tll me.