The Pendulum Lab – Measuring g the Fun Way

The acceleration due to gravity, g, is one of the most important constants in physics. While we often take its value as 9.8 m/s², students can measure it themselves using one of the simplest experiments in the lab — a swinging pendulum.

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The Setup

• Tie a small mass (a bob) to a piece of string.

• Fix the string so the bob can swing freely.

• Measure the length, L, from the pivot to the centre of the bob.

• Displace the pendulum slightly and let it swing.

• Time how long it takes to complete 10 oscillations, then calculate the period, T (time for one swing).

The relationship between period and length is:

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Which rearranges to:

$$g = \frac{4\pi^2 L}{T^2}$$

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Sample Results

Length L (m)	Time for 10 swings (s)	Period T (s)	Calculated g (m/s²)
0.20	9.0	0.90	9.7
0.40	12.7	1.27	9.8
0.60	15.5	1.55	9.8
0.80	17.9	1.79	9.9
1.00	20.0	2.00	9.9

By plotting $T^2$ against L, students obtain a straight line with slope $4\pi^2 / g$. From the slope, g can be calculated with good accuracy.

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Why It Works in Teaching

• Simple to set up, yet powerful in results.

• Introduces careful timing and averaging to reduce error.

• Shows how graphs can be used to extract constants from experimental data.

• Reinforces the importance of precision — small timing mistakes make a big difference.

Students enjoy the experiment because it feels tangible: they measure something as fundamental as gravity using nothing more than a string, a weight, and a stopwatch.