I genuinely don't know how to do this question
Here's my explanation, use it with Rui's
We need to know first about electromagnetic induction.
A conductor that experiences a changing magnetic flux will have a current induced through it. This current is a manifestation of the conservation of energy (but that isn't necessary to explain here). The current acts to establish a new magnetic field (remember all currents are surrounded by a magnetic field), and according to Lenz's Law, this magnetic field will act in the opposite direction to the one that created it. That is, it
opposes the change that created it.
Now when the switch is closed, it is a
direct current that flows through the spring. Normally, we don't associate direct currents with changing magnetic fields and electromagnetic induction, since the current flows in a single direction and so establishes a constant magnetic field, not a changing one. However, that's long term - There is still a brief moment where the magnetic field around the spring changes. As the current goes from nothing, to something, that causes a changing magnetic field. This is the tough bit to understand - If it's a little confusing let me know!
We don't really care about direction in this scenario. The spring acts as a solenoid, and as the current through it increases, that creates a changing magnetic field. The iron rod experiences this changing magnetic field and will briefly have currents induced through it (
eddy currents). These currents create a new magnetic field, and this interacts with the magnetic field of the spring to exert a force which causes it to bounce. Kind of like a bar magnet pushing on another bar magnet, sort of. This interaction is
very quick, it only happens as the current begins flowing through the spring. Once it is flowing properly the force on the spring is gone.
If you want to get super technical, the movement of the bouncing spring may cause the rod to experience another small change in magnetic flux which could cause another force. However, this process wouldn't sustain itself (you'd lose energy to heat in the rod and the bouncing would fade away anyway)