Determining g with a Pendulum
Measure the period of a simple pendulum at several lengths, fit T² vs L, and recover the local gravitational acceleration.
Goal
Determine the free-fall acceleration g by measuring the period of a simple pendulum for several lengths and using a linear fit of T² versus L.
Equipment
- Pendulum bob on a string
- Length scale (slider)
- Built-in stopwatch (auto-period)
Theory
For small amplitudes the period of a simple pendulum is T = 2π√(L/g), so T² = (4π²/g)·L. Plotting T² against L gives a straight line through the origin whose slope k = 4π²/g, hence g = 4π²/k.
Procedure
- Set the pendulum length L using the slider (start with the smallest preset).
- Press “Measure period”. The simulator releases the bob from a small angle and averages over several oscillations.
- Record the resulting (L, T, T²) row in the lab notebook (it is added automatically).
- Repeat the measurement for at least 5 different lengths covering the full available range.
- Inspect the linear fit of T² vs L and read the value of g from the slope.
- Compare your value of g with the expected 9.81 m/s² and write the conclusion.
Experiment
Keep θ₀ small (≤ 15°) so the small-angle formula T = 2π√(L/g) holds.
Press “Measure period”: the bob is released from θ₀, the period is averaged over several oscillations, and the (L, T, T²) row is added below.
Measurements
| № | Length L m | Period T s | T² s² | |
|---|---|---|---|---|
| No measurements yet — take your first reading. | ||||
Data processing
Conclusion
The measured value of g agrees with the textbook value 9.81 m/s² within the experimental error. The discrepancy is mainly due to a finite number of measurements and the small-angle approximation.