Pendulum of length 0.9 m: its period

A simple pendulum has a length of 0.9 meters, with g equal to 10 meters per second squared. Find its period.

Step-by-step

1. T = 2π√(L/g) = 2π√(0.9/10) ≈ 1.885
   For small swings a pendulum's period depends only on its length and gravity

Why it works

When a simple pendulum undergoes simple harmonic motion, its period depends only on the length and gravitational acceleration, not on the mass of the bob or the amplitude. This is called isochronism. The period is directly proportional to the square root of the length and inversely proportional to the square root of gravitational acceleration, so the period doubles only when the length becomes four times as long. This property is the basis for pendulum clocks to keep time.

Common mistakes

• Including the mass of the bob or amplitude in the period formula, assuming they have an effect.
• Writing the square root relationship as a direct or inverse proportion, omitting the radical sign.
• Mismatching the value of gravitational acceleration with length units, such as using centimeters with 9.8.

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