Simple Pendulum

Simple pendulum: a point mass m suspended from a massless string of length L, swinging under gravity.

For small angles (θ < ~15°), sin θ ≈ θ ⇒ motion is approximately SHM.

Equation of motion (small angle): θ̈ + (g/L)·θ = 0 ⇒ ω = √(g/L).

Period T = 2π·√(L/g). Independent of mass m and amplitude (for small angles).

T depends on L and g — does NOT depend on mass m of the bob.

Long pendulums swing slowly; short ones swing fast.

At higher altitudes or at the equator: g lower ⇒ T longer.

Foucault pendulum: long pendulum demonstrates Earth's rotation as its swing plane appears to rotate.