A physics student investigates how the period of a horizontal spring–mass oscillator depends on the attached mass. Using a force sensor to verify that the spring obeys Hooke’s law, the student measures the period for several different masses while keeping the same spring. The results are shown below.
Mass m (kg) | Measured period T (s)
0.10 | 0.63
0.20 | 0.89
0.30 | 1.09
0.40 | 1.26
(1) Demonstrate quantitatively that the data are consistent with a proportional relationship between T2 and m. Explicitly calculate T2 for each trial and comment on the trend.
(2) Assuming the proportionality is exact, determine the numerical value of the spring constant k. Outline how you obtained the result from the data.
(3) Using your value of k, estimate the expected period for a 0.60kg mass on the same spring. Show calculations and express your answer to two significant figures.
(4) Identify one plausible experimental source of error that could cause slight deviations from perfect proportionality in the data, and explain qualitatively how it would affect the measured periods.