Pendulum

Swing time depends on length, not on weight — Galileo's discovery.

A pendulum's swing time depends on its length, not its mass — Galileo's discovery.

Try this

pendulum length L (m) — watch the swing period (g ≈ 9.8)

T = 2π√(L/g) seconds = 2.01

Pendulum — change the length, watch the period

Length L 2.0 m

period T = 2π√(L/g) = 2.84 s for L = 2.0 m — it doesn't depend on the bob's mass, nor (for small swings) on the amplitude

Period of a simple pendulum

T = 2 π \cdot L / g

Notice what's *missing*: mass and (for small swings) amplitude. Quadruple the length and the period only doubles.

Your turn

Roughly how long must a pendulum be to tick once per second (period 2 s)?

Galileo timed swinging lamps against his own pulse and noticed the period didn't depend on how wide they swung — long before stopwatches existed.

Period

T = 2 π L / g

Galileo timed pendulums against his pulse — and figured this out before there were stopwatches.