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I suspect that the "magnetic braking" effect of eddy currents must play a
role in the case of the magnet falling near the copper winding. The effect
may be small but not negligible. Local current loops can exist in short
segments of copper, even when the input resistance of the oscilloscope
is very large. Just recall what happens when a magnet falls through a
copper pipe which has a slot from one end to another. The magnetic braking
is nearly as strong as it is in a pipe without a slot. I have a setup to
demonstrate this.