The method and the results are on the simple harmonic motion lab. Do the analysis yourself first, then check the answers below.
Quick answer: Simple harmonic motion is repeated oscillation where the acceleration is proportional to the displacement from equilibrium and points towards it, a = −ω²x. These answers go with the Physics 11-12 lab on simple harmonic motion: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
Model answers use the sample table. Your own results will differ slightly, but the gradient, the intercept and the conclusions should follow the same pattern if your timing is careful.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB C.1
Timing 20 oscillations reduces the effect of reaction time on each period. For m = 0.300 kg, T = 15.6 ÷ 20 = 0.780 s and T² = 0.608 s².
Question 2 Uncertainty in the timing
Percentage uncertainty in t = 0.2 ÷ 12.9 × 100 = 1.6 %, the same for T. T² doubles this: 3.1 %.
Question 3 Plot and gradient
Gradient = (1.010 − 0.216) ÷ (0.500 − 0.100) = 0.7938 ÷ 0.400 = 1.98 s²/kg. The points lie close to a straight line.
Question 4 Spring stiffness
gradient = 4π²/k, so k = 4π² ÷ 1.98 = 39.48 ÷ 1.98 = 19.9 N/m.
Question 5 The intercept
Using the first point, intercept = 0.216 − 1.98 × 0.100 = 0.018 s². The spring itself oscillates, so the effective mass is m + ms/3, which shifts the line. Intercept ÷ gradient = ms/3 = 0.009 kg, so the spring mass is about 27 g.
Question 6 Testing proportionality
If T ∝ m, then T/m would be constant: for 0.100 kg it is 4.65 s/kg and for 0.500 kg it is 2.01 s/kg, so it is not constant. The graph of T² against m is straight, so T² is proportional to (m + ms/3), that is T ∝ √m.
Question 7 Amplitude check
Use one mass, time 20 oscillations for starting displacements of 1 cm, 2 cm and 4 cm (all small), and repeat each. The times should agree within the timing uncertainty, so the period is independent of amplitude.
Question 8 Improvements
Use a motion sensor or video with a frame counter to find the period more precisely, and repeat each measurement three times to find a mean. Start timing at the equilibrium marker, where the speed is greatest, so the start and stop moments are sharper. Always use small amplitudes without swaying.
