KinexiaLEARN PHYSICS

Pendulum Period — Grandfather Clock (Worked Example)

Easy
Problem

A grandfather clock uses a pendulum of length 1.0 m. What is its period? (g = 9.8 m/s², small-angle swings)

Given

  • L = 1.0 m

  • g = 9.8 m/s²

Find

The period T.

Principle

For small angles a pendulum is a simple harmonic oscillator with period T = 2π√(L/g) — set by length and gravity, not mass or amplitude.

Formula

Solution

  1. Write the formula: T=2πL/gT = 2\pi\sqrt{L/g}

  2. Substitute: T=2π1.0/9.8T = 2\pi\sqrt{1.0/9.8}

  3. Inside the root: 1.0/9.8=0.1021.0/9.8 = 0.102; 0.102=0.319\sqrt{0.102} = 0.319

  4. Multiply: T=2π×0.319=2.01 sT = 2\pi \times 0.319 = 2.01\ \mathrm{s}

2.01 s

Unit check

√(m ÷ m/s²) = √(s²) = s — a time, correct.

What this means physically

2.01 s — essentially 2 seconds, which is why 'seconds pendulums' are about a metre long. Each half-swing takes 1 s, so the clock ticks once per second.

Common mistake

Using the mass of the bob. The period formula has no m — mass cancels out, so a heavy and light bob swing together.