// mechanics · T = 2π√(L/g)

Simple Pendulum

Adjust the length and press Start — or use the stopwatch to time oscillations
stopwatch
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Length 80 cm
Amplitude 15°
Gravity

Use the stopwatch to time oscillations, or calculate directly with T = 2π√(L/g).

About the simple pendulum

  1. Setup. A small, heavy bob hangs from a fixed pivot by a light, inextensible string. It is displaced to a small angle and released.
  2. Time period. For small angles (< 15°), T = 2π√(L/g), where L is the distance from the pivot to the centre of mass of the bob.
  3. Measuring L. Use a metre rule from the pivot to the centre of the bob. If you measure to the bottom, subtract the bob's radius to get L.
  4. Measuring T. Time N complete oscillations (say 20) and divide the total by N. This averages out timing errors.
  5. Finding g. Record T for several lengths. Plot T² vs L — the graph is a straight line through the origin with slope 4π²/g, so g = 4π²/slope.
  6. Assumptions. Small angle, no air resistance, point-mass bob, rigid support, inextensible string.
💡 In Explore mode, adjust the length and gravity, then press Start. Record data points at different lengths and watch the T² vs L graph build up!