Simple Pendulum: Measuring g
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flagWhat you'll discover
- arrow_forwardUse T = 2π√(L/g) to design a measurement of g
- arrow_forwardTime 20 oscillations and compute the period accurately
- arrow_forwardPlot L versus T² and extract g from the slope
- arrow_forwardExplain why timing many oscillations beats timing one
- arrow_forwardIdentify human reaction time as the dominant random error
The physics: a clock made of string
For small swings (under about 10°), a simple pendulum is a harmonic oscillator with period T = 2π√(L/g), where L is measured from the support to the CENTRE of the bob. Squaring gives T² = (4π²/g)L — so a graph of T² against L is a straight line through the origin with slope 4π²/g.
That graph is the heart of the experiment: g = 4π²/slope. Using the slope of several points instead of a single reading cancels random errors and exposes any systematic offset (a line that misses the origin hints you measured L to the top of the bob, not its centre).
Procedure: why 20 oscillations?
Your thumb on the stopwatch is good to about ±0.2 s. If you time a single 1.8 s oscillation, that is an 11% error — useless. Time 20 oscillations (≈36 s) and the same ±0.2 s shrinks to 0.5%: the trick is dividing one reaction error across many periods, T = t/20.
Start counting as the bob passes the LOWEST point — it moves fastest there, so your judgement of the crossing is sharpest. Count "zero" when you start the watch (a classic blunder is counting "one"). Repeat for five or six lengths between 40 cm and 120 cm and record everything in a table before graphing.
Errors and precautions
Keep the amplitude small: at 15° the period is already about 0.4% longer than the small-angle formula, and the error grows with angle. Use an inextensible thread and a heavy, small bob so air drag and thread stretch stay negligible. Measure L with a metre ruler to the bob centre — add the bob radius to the thread length.
In Kathmandu g ≈ 9.79-9.81 m/s² depending on altitude. If your value lands within a few percent of that, your technique is sound. For the report: reaction time at start and stop, amplitude too large, fan or wind disturbing the bob, and support not rigid are the four standard sources of error.