I am sure you have seen the flashlights that you shake to charge. I know they function by building a charge off of a magnet moving through a magnetic coil. I was wondering what the formula for the amount of electricity generated by this for every up and down (as one unit)? Also, what is a good ball park on force it takes to pass the magnet through the coil and what is an easy/typical base variable(s) to start from? (such as, # of coils = 100 vs 57)

The basic concept is Faraday's law of induction, that you will induce a voltage that is proportional to how fast the magnetic flux is changing; the latter is dependent on the strength of the magnet and how fast you shake it. The current will then depend on the resistance of the circuit.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html