Simple pendulum: measuring g
Time a swinging pendulum at five lengths, plot T² against L, and extract the acceleration due to gravity from the gradient. Expect within 2% of 9.81 m/s².
WHAT YOU'LL LEARN
- ✓Reducing timing error by timing 20 oscillations, not one
- ✓Linearising an equation: why T² vs L gives a straight line
- ✓Extracting a physical constant from a graph gradient
ON YOUR BENCH
- □Retort stand, clamp and split cork
- □Light string (~1.2 m) and pendulum bob
- □Stopwatch, metre rule
- □Graph paper
The protocol, step by step
The same guide is printed and waiting at your bench.
- 01
Set up and measure length
Clamp the string between the split cork so the pivot point is sharp. Measure L from the pivot to the centre of the bob — half the bob's diameter matters, so measure to the middle, not the top.
- 02
Small swings only
Displace the bob less than 10° and release without pushing. The simple pendulum formula assumes small angles; big dramatic swings quietly break it.
- 03
Time 20 oscillations
Start the stopwatch as the bob passes the lowest point (a fiducial marker behind it helps), count 20 complete oscillations, and stop. Divide by 20 for the period T. Repeat and average.
- 04
Vary the length
Repeat for L = 0.40, 0.60, 0.80, 1.00 and 1.20 m, recording T for each.
- 05
Plot T² against L
Since T = 2π√(L/g), squaring gives T² = (4π²/g)·L — a straight line through the origin with gradient 4π²/g. So g = 4π² ÷ gradient.
What you should see
- →A straight line through the origin on the T²–L plot. A non-zero intercept usually means a length measurement offset — often forgetting the bob's radius.
- →Gradient close to 4.03 s²/m, giving g ≈ 9.8 m/s². Nairobi's value is about 9.79 m/s² — being 1,700 m up and near the equator both shave a little off.
- →Timing by hand adds ±0.2 s per measurement; spread over 20 oscillations that's only ±0.01 s on T. That's the whole point of counting 20.
| L /m | 0.40 | 0.60 | 0.80 | 1.00 | 1.20 |
|---|---|---|---|---|---|
| T /s | 1.27 | 1.56 | 1.79 | 2.01 | 2.20 |
| T² /s² | 1.61 | 2.43 | 3.20 | 4.04 | 4.84 |
⚠ BEFORE YOU START
- •Clamp the stand near the bench edge or weight the base — a metre-long pendulum can pull a light stand over.
- •Keep the swing plane clear of other students and glassware.
Try it, then run it for real.
Practise the whole thing on the virtual bench, then book real lab time and do it with your own hands.