Magnet Shake Generator - how to replicate in LTspice?
The easiest way to do this would be to make measurements of voltage and current from the coil and then present that to LT spice as an AC voltage source or a pulsed source.
If you wanted more detail, you could run a motor simulation like this:

Source: https://www.precisionmicrodrives.com/content/ab-025-using-spice-to-model-dc-motors/
The motor coil pictured above could be the calculated inductance of the shake coil, and the back emf could be the voltage generated from the magnet moving past the coil.