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The launcher consists of a striker connected to the spring... when the spring is pulled back and let go the strike moves forward and hit the projectile.

i have the vertical distance of the launch, the mass of both the launcher system (mass of spring + mass of striker), mass of the projectile, the distance the projectile needs to travel and also the spring constant (k),

so far... i have:

Kinetic Energy (launcher) + Elastic Potential Energy = Kinetic Energy (projectile)

problem i run into... is that i can't simplify the equation ... i get to:

Mlauncher*Vlauncher^2 + k*x^2 = Mprojectile*Vprojectile^2

Vprojectile = deltaX / time

time = SquareRoot[DeltaY/(g/2)] g = 9.8m/s^2

Vlauncher = (Mprojectile * Vprojectile) / Mlauncher

i need to make an equation that allows me to solve for x (spring extension).... but i just can't simplify it properly.... If anyone could help me out, it would be greatly appreciated. Thanks.

By the way, is there a general formula to calibrate something like this?