I think the reality of your wave pulse is going to depend on the exact geometry of the magnet and the coil, and neither is simple. The magnet in particular will not be uniform, and will not be a uniform position from the coil. So you'd have to break it all up and do a finite element analysis. Not easy to set up, even with plenty of processing power to do the work.
In other words, I would not expect a precise sine wave. There's no reason to expect one. For a rotating system, maybe.
In other words, I would not expect a precise sine wave. There's no reason to expect one. For a rotating system, maybe.