0.98 m pendulum when g = 9.8: the period

A simple pendulum 0.98 m long swings through a small angle at a place where g = 9.8 m/s². Find its period.

Step-by-step

1. T = 2π√(L/g) = 2π√(0.98/9.8) ≈ 1.9869
   For small swings a pendulum's period depends only on its length and gravity

Why it works

The period of a small-angle pendulum, T = 2π√(L/g), grows when g is smaller, which is why the same pendulum swings more slowly on the Moon than on Earth.

Common mistakes

• Substituting g = 10 out of habit instead of the 9.8 m/s² given in the problem.
• Assuming a pendulum about 1 m long always has a period of exactly 2 s, which needs g ≈ 9.87 m/s².

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