Quoted from flynnibus:
2) Slop in the flipper movement is a loss of transferred kinetic energy to the intended load, not a new load. The slop is periods where the plunger is getting less resistance as it's pushing against less when it's pushing against nothing or off axis. There isn't any 'compensation' for this loss where the coil is being driven harder to make-up for it.. the lost kinetic transfer is just lost to the inconsistent movement. The coil was driven the same.. the magnetic field was the same.. it's just how consistently that linear movement is applied to the intended load.
TL;DR version:
Load matters on a coil. More load, higher power and temperatures. 'cause, physics.
How do I know? Inductive reasoning.
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detailed and boring version:
What you need to add to this discussion is back EMF generated in the windings due to the mechanical load. If there's greater mechanical resistance to plunger movement, it will generate additional current in the coil via back EMF. So it's not quite accurate to say "the coil was driven the same". Actually, the coil sees higher currents (drive + back EMF) when there's greater resistance in the plunger. The load is said to "induce" a current in the coil (and this effect is also the principle for the common component known as the inductor).
Stated another way, there's no free lunch. Electric motors and coils obey the laws of conservation of energy just like everything else. The power to drive a motor (or a coil) is not just a function of motor speed. It depends on the resistance of the load.*
More load = more work (force x distance) = more power input from the windings. Given that power (the product of voltage x current) into the coils must increase, so too will the heat generation as defined by coil resistance. It just so happens the way nature balances the energy in coils and motors under varying loads is via back EMF. It must be this way, as shown in Maxwell's laws for EM.
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*to cite the dreaded automotive example, this is why an electric car going a constant speed on a flat stretch of road uses less power than the same car at the same speed going uphill. The difference here (at the same motor speed) is the load. Higher load = more power = more current = higher motor (and battery) temperatures.