I have taken the challenge to measure the earth's gravitational force, g, without knowing the mass of an object. To do this, we took a spring and had it oscillate vertically and determined the period T. Here is my theoretical development: F = -kx x(t) = Acos(ωt+θ) where ω = √(k/m) of course, ω is the angular frequency and can be written as 2π/T so let's isolate m. m = k*T^2/4π^2 adding this into hooke's law, g = -kx/(k*T^2/4π^2) and therefor g = 4π^2*x/T^2 That's a very nice formula until you end up testing it. With a little work, we determined the measurement of g was always off by a factor of 1/T and therefor the formula should be g = 4π^2*x/T^3. Where does this extra T come from? We've been trying to figure this out for a long time.