Classical Mechanics & Geodesy

Kater's Reversible Pendulum

Simulate Henry Kater's 1817 reversible pendulum for measuring freefall acceleration $g$. By adjusting sliding counterweights until the period from pivot $O_1$ equals pivot $O_2$, $g = 4\pi^2 L / T^2$ is determined with extreme precision.

Active Pivot Pivot O₁ (Upright)

Period T₁ 2.006 s

Period T₂ 2.012 s

Calculated g 9.808 m/s²

Mass & Pivot Controls

Large Mass Position y₁ 120 mm

Fine Tuning Mass y₂ 340 mm

Visual Overlay

Show Pivot & Center of Mass Badges

Show Tangent Velocity & Gravity Vectors

Show Pendulum Swing Path Trail

Controls

Kater's Gravity Formula

Physical Pendulum Period: T = 2π √(I / m·g·h)
Reversible Condition (T₁ = T₂): g = 4π² L / T²
where L = d(O₁, O₂) is the distance between the knife-edge pivots.

Developer Reference

Core Algorithm & Standalone Script

// Kater's reversible pendulum physical engine
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// g = 4 * pi^2 * L / T^2