Simple Pendulum
BINAS 35B1Tsokos Ch. 9.3
Overview
A simple pendulum of length L oscillates with period T = 2π√(L/g). Valid only for small angles (< ~10°). Period depends only on L and g — NOT on mass, NOT on amplitude (for small angles). To increase period: increase length or go to a weaker gravitational field. On the Moon, a pendulum swings more slowly.
Simple pendulum
A simple pendulum consists of a mass (bob) on a string of length L. For small angles (θ < 15°), the restoring force component is approximately F ≈ −mg sin θ ≈ −mgθ (radians), which gives SHM with T = 2π√(L/g). The period depends ONLY on L and g — not on mass or amplitude (for small angles). Longer pendulum → slower oscillation.
Worked Examples
Common Mistakes
- ⚠Including mass in the pendulum period formula — it doesn't appear
- ⚠Assuming large-angle pendulums still follow T = 2π√(L/g) — this only works for small angles