- #1
charbon
- 23
- 0
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.
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.