In our lab, we are trying to verify the properties of SHM using a mass spring system. (Verify that amplitude and angle do not matter). We based it on T = 2pi*sqrt(m/k)
One system is the vertical one and the other is on an inclined plane.
We graphed mg vs. x and T^2 vs m and the slopes give us "k" and "4pi^2/k
The only reason we used graphs was because we couldn't pull down the same spring and mass by the same amount for both the inclined and vertical systems. (Pulling the spring down even more on the vertical system would cause the spring is jerk).
We're not sure how we can use the slopes to prove that amp and orientation of the spring don't affect it's period, though.