Same real phenomenon as the 3D version — equal-length pendulums coupled only through a shared, spring-mounted rail of finite mass M — but simplified to the small-angle (linearized) regime, a standard and legitimate reduction of the same Lagrangian used when swings stay modest:
θᵢ'' = -(g/L)θᵢ - a/L - c·θᵢ'
a = [ Σᵢ m(g·θᵢ + L·c·θᵢ') - k·x - cᵦ·ẋ ] / M
Dropping sinθ≈θ, cosθ≈1 turns the beam's effective inertia into just M (instead of M plus a swing-dependent term), a genuinely different — simpler — model from the full nonlinear 3D one, not a flattened reprojection of it. It still captures the real Huygens effect: random-phase pendulums exchange energy through rail motion and settle into a shared rhythm.
Click a bob to kick it out of rhythm; drag empty canvas to pan, scroll to zoom.