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 (SHM) is repeating motion in which the net force is proportional to the displacement from equilibrium and points back toward it, F = −kx. These answers go with the AP Physics 1 lab on simple harmonic motion: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample data. Your own values will differ slightly, so compare the method and the form of the result, and compare your g with 9.81 m/s².
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 7
Timing one swing (about 1.5 s) with a reaction time of 0.2 s gives roughly 13 % uncertainty; timing 20 swings (about 30 s) reduces it to under 1 %. Starting at the marker, where the bob moves fastest, makes the start and stop moments easier to judge. 20 swings reduces the percentage uncertainty about twenty-fold.
Question 2 Check the table
T = 33.5 ÷ 20 = 1.675 s and T² = 1.675² = 2.806 s², which agrees with the table.
Question 3 Plot and describe
The points lie on a straight line through (or very near) the origin. This shows T² is directly proportional to L, so T is proportional to √L, as T = 2π√(L/g) predicts.
For small angles T does not depend on amplitude, so T stays unchanged. It also does not depend on the mass, because the mass cancels from the equation, so a bob twice as heavy gives the same period.
Question 7 Improving the lab
Sources: (1) the length L is hard to measure to the centre of the bob, and (2) timing at the marker has human reaction error. Improvements: measure L with a rule to the bob’s centre using the bob’s diameter, and film the swing and time it from the video frames (or use more oscillations and repeat each length three times).
