Before you touch the controls
Predict what doubling the length and doubling the mass will each do to the period. Explain your reasoning before running the experiment.
Change one thing at a time
- Set a small release angle, for example 5°, and keep gravity and damping fixed. Use zero damping when testing the ideal relationship.
- Start the pendulum. Measure several complete oscillations and divide the elapsed time by the number of oscillations to estimate the period.
- Repeat for at least four lengths. Record T and calculate T². Keep the mass and release angle constant.
- Return to the original length and change the mass. Compare the period. Finally try a larger angle and inspect where the small-angle model becomes less useful.
Record your observations
| Length L | Number of oscillations | Elapsed time | Period T and T² |
|---|---|---|---|
| Trial 1 | — | — | — |
| Trial 2 | — | — | — |
| Trial 3 | — | — | — |
| Trial 4 | — | — | — |
Use this table as a worksheet, or record the available measurements in the lab notebook. Export your observations before refreshing or closing the lab.
Turn measurements into an explanation
- Is T² proportional to L? What would a graph of T² against L look like?
- Does doubling the length double the period? Compare with T = 2π√(L/g).
- Which parts of the real apparatus might introduce measurement error?
Think about the model
T = 2π√(L/g) assumes a small angular displacement and an ideal pendulum. Larger amplitudes and damping require attention to the model used.
Take it further
Compare the same pendulum under different gravitational accelerations. Predict the ratio of periods before changing gravity.