Huygens Clocks - Coupled Pendulum Synchronization

Explore the fascinating synchronization phenomenon discovered by Christiaan Huygens in 1673

Theoretical Background

Kuramoto Model:

dθᵢ/dt = ωᵢ + (K/N) × Σⱼ sin(θⱼ - θᵢ)

In 1673, Dutch physicist Christiaan Huygens discovered that two pendulum clocks hanging on the same beam would spontaneously synchronize, even when started with opposite phases. This phenomenon, called subharmonic synchronization or clock synchronization, is one of the most classic examples of coupled oscillator synchronization in nature.

Time: 0.00s
Sync Level: 0.00

Phase Difference Heatmap

Fourier Spectrum

Controls

5
2.0
0.10
0.010

Observation Guide

  • Start with low coupling strength (K ≈ 0) to observe independent pendulum motion
  • Gradually increase K to observe the transition to synchronization
  • When K exceeds the critical value, phases will automatically lock into synchronization
  • The phase difference heatmap shows the synchronization state in real-time
  • The Fourier spectrum reveals the frequency components and harmonic relationships

Current Parameters