Question

A single spring with a 0.75 kg mass on it is stretched out and then released. Then the velocity of the mass is measured as the spring passes through its equilibrium position. This experiment is repeated 18 times; pulling the spring to a different distance each time. The amplitudes and speeds are listed below.

Amplitude (m.)	Speed at Equilibrium (m/s)
0.05	0.23
0.10	0.38
0.15	0.60
0.20	0.84
0.25	0.98
0.30	1.14
0.35	1.49
0.40	1.63
0.45	1.82
0.50	2.30
0.55	2.34
0.60	2.40
0.65	2.69
0.70	2.54
0.75	2.80
0.80	3.08
0.85	3.33
0.90	3.49

Calculate the spring constant of the spring and give uncertainty so that you can be 95% sure that the true value of the spring lies within the range you give.
k = ± N/m

Now calculate the spring constant and give uncertainty so that you can be 95% sure that the spring constant calculated from any single performance of the experiment (as opposed to doing it multiple times as above) will fall within the range given.
k = ± N/m​

Answer 1