Simple Pendulum

Point mass at the end of a massless rigid rod, fixed pivot. g = 9,81 m/s²; F_g and R are vertical and opposite.

L (m)0,2–10 m

m (kg)0,1–50 kg

θ₀ (°)−179…179

Slow ×1…5 (1 = real speed, 5 = ⅕ speed)

Pivot friction f0 · 0,005 · 0,01 · 0,02

running

θ—

ω—

t—

T—f = 1/T—

T measured from the simulation: 2×Δt between successive turning points · f = 1/T

K—U—

E—v—

K = ½·m·v² · U = m·g·L·(1−cos θ)

|p|—

pₓ—py—

kg·m/s · |p| = m·L·ω, tangent to the trajectory

|F_g|—

along the rod—perpendicular—

N · mg·cos θ / mg·sin θ, vertical downward

|R|—

along the rod—perpendicular—

N · opposite to F_g, applied at the pivot

Note: due to floating-point rounding, the motion will eventually damp over long periods even when pivot friction is 0.