Least-Action Pedagogy: 1D Rope as Coupled Oscillators

Number of oscillators (N)

Neighbor coupling (K)

Frequency spread (σ)

Damping (γ)

Noise (η)

Amplitude (display)

Time step (dt)

Initial condition

Cluster threshold (Δθ)

Global order (R)

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Clusters

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Mean |Δθ|

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Mode

Free ends

What students can do:
1) Start low K → no coherence. Increase K slowly until local locking appears.
2) Watch clusters merge → a “least-effort” resolution of phase disagreements.
3) Contrast free ends vs pinned ends to see boundary conditions as “constraints.”

Interpretation you can say out loud: the “path” here is the rope’s phase pattern. No particle is the protagonist—constraints and coupling are.

Drag on the plot to locally perturb phase.

fps: –

phase (color) / coherence (line smoothness)

clusters highlighted as bands below rope