Cylinder Magnet Passing through a solenoid

[ALine]

If I were to pass a cylindrical magnet through a solenoid, what would the induced current and voltage look like if I were to connect the two wires forming the solenoid. 

Also, how would I calculate this based on the magnetics magnetic field strength, volume and mass of the magnet, number of windings of the solenoid, length of the solenoid, and area of the solenoid and velocity that the bar magnet is traveling through? Creating a single relational equation.

 

[Externet]

I suspect the waveform on the oscilloscope will be like

And the speed of the magnet altering the amplitude, the strength of the magnet the time of the sweep, with other influences as gap dimension, size and shape of magnet, size and shape of bobbin, wire diameter, electrical load...

I have a couple of these ----> https://www.amazon.com/Shake-Light-40-Rechargeable-Flashlight/dp/B00HS5M706/ref=asc_df_B00HS5M706/?tag=hyprod-20&linkCode=df0&hvadid=167133658256&hvpos=&hvnetw=g&hvrand=3518713909556488795&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9014290&hvtargid=pla-307268559308&psc=1

Which works as you describe with rectifier, large capacitor and led emitter.

To express a formula; I would need a new brain transplanted as the last one I got was refurbished and do not recommend such, does not work well.

Meanwhile, check ---> https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-faradays-law

and similar sites addressing mister Faraday

Edited June 1, 2022 by Externet
Added the source of the graph.

[ALine]

Thanks!