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. This AP Physics 1 lab on simple harmonic motion gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How does the period of a pendulum depend on its length, and can a few pieces of string and a stopwatch give a good value for g? You measure the time for 20 oscillations at five lengths, plot T² against L and use the gradient to calculate the gravitational field strength.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 7
Aim
To investigate how the period of a simple pendulum depends on its length and to use the results to find the gravitational field strength g.
Equipment
- Thread about 1.5 m long and a small dense bob (for example a metal nut or a key)
- Clamp and stand, or a firm table edge
- Metre rule and a stopwatch or phone timer
- Protractor or a printed 10° mark, and a small fixed marker at the centre
Safety
Keep the stand stable and clamp it to the bench. Keep the swing area clear of faces and fragile items. Do not use a heavy bob.
Method
- Tie the bob to the thread and clamp the other end so that the length L from the pivot to the centre of the bob is 0.300 m. Measure L carefully.
- Pull the bob aside through no more than 10° and release it without pushing.
- Start the stopwatch as the bob passes the marker, then count 20 complete oscillations and record the time t.
- Repeat for L = 0.500, 0.700, 0.900 and 1.100 m.
- Calculate the period T = t ÷ 20 and then T² for each length.
Results
Sample measurements taken by a student:
| L / m | time for 20 oscillations t / s | T / s | T² / s² |
|---|---|---|---|
| 0.300 | 22.0 | 1.100 | 1.210 |
| 0.500 | 28.4 | 1.420 | 2.016 |
| 0.700 | 33.5 | 1.675 | 2.806 |
| 0.900 | 38.2 | 1.910 | 3.648 |
| 1.100 | 42.0 | 2.100 | 4.410 |
Analysis questions
Question 1 Why time many swings
Explain why the student times 20 oscillations instead of one, and why the timing starts at the marker.Question 2 Check the table
Verify the T and T² values in the row L = 0.700 m.Question 3 Plot and describe
Plot T² (vertical axis) against L (horizontal axis). Describe the graph and say what it shows about the relationship between T and L.Question 4 Gradient
Use a large triangle on the line of best fit, for example the first and last points, to find the gradient with its unit.Question 5 Value of g
The theory gives T² = (4π²/g)L. Use your gradient to calculate g and the percentage difference from 9.81 m/s².Question 6 Amplitude and mass
State what you expect to happen to T if the starting angle is 5° instead of 10°, and if the bob is twice as heavy. Justify each answer.Question 7 Improving the lab
Suggest two sources of error and one improvement for each.
