Simple pendulum L = 0.4 m: its period

A simple pendulum 0.4 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√(0.4/10) ≈ 1.2566
   For small swings a pendulum's period depends only on its length and gravity

Why it works

A small-angle pendulum obeys T = 2π√(L/g). The length sits inside the square root, so a shorter string gives a shorter period and the period is never proportional to the length itself.

Common mistakes

• Writing T = 2π√(g/L), with L and g the wrong way round.
• Assuming the period is proportional to the length instead of to its square root.

Related

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