Barry Hansen enthusiasm for Coilgun Designs has created an EE education portal.
See the RLC Simulator and Inductor Simulator. By building a Gauss Gun which is like a Solenoid, Electromagnetic Relay or 3 phase contacter, you can learn electromechanics. This may be like a sequential solenoid which makes things move.This leads us to the Linear motor.
There is also a very interesting learning article. PID in Control Systems in reading a DIY levitator design In Popular Electronics May 1996 - James Cicon.
Why build a coilgun?
It demonstrates many basic concepts of magnetic machines. A coilgun is foremost an example of a solenoid. These appear practically everywhere, from car door locks to doorbells.
(Youngsters Should do Basic Electricity Experiments with the Supervision and Guidance of a Technician, Engineer, Experienced Enthusiast or an Amateur-Radio Operator
My own interest into electricity-magnetism came with a failed Doorbell in my Schooldays, from collecting gramophone and chemistry lab parts i got escalated to the Iron-n-Copper Age - delabs)