Pendulum of length 2 m: find its period

A simple pendulum 2 m long swings through a small angle (g = 10 m/s²). Find the period of one complete oscillation.

Step-by-step

1. T = 2π√(L/g) = 2π√(2/10) ≈ 2.8099
   For small swings a pendulum's period depends only on its length and gravity

Why it works

For a small-angle pendulum T = 2π√(L/g), so the period depends on the length and g alone. In this case L/g = 0.2, whose square root is not a terminating decimal.

Common mistakes

• Rounding √0.2 to 0.4 and reporting a period that is too small.
• Forgetting that the result is a full back-and-forth time, not a half swing.

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