Simple Pendulum Period
Simple Pendulum Period
A pendulum’s period depends only on its length and gravity, not its mass or (for small swings) its amplitude — which is why it keeps time.
The period is T = 2π·√(L/g). where L is the pendulum length and g gravity.
Inputs
L := 1 m=1 m
g := 9.81 m/s^2=9.81 m/s^2
Apply the simple-pendulum period formula.
T := 2·pi·sqrt(L/g)=2.01 s
Results
A one-metre pendulum swings in about two seconds. Lengthening it slows the swing; the independence from mass is what makes it a reliable clock element.
Assumptions & limitations
- Small-amplitude swing.
- Point mass on a massless rod.
- No air resistance or pivot friction.