Damped Harmonic Oscillator

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In plain English

Same power-law trend, plus a sine that slowly fades (damps) as the years pass — booms and busts that get a bit quieter versus the trend, if that story holds.

If the collector already built the harmonic-gap model, this page shows that. Otherwise it fits a 1460-day sine to the residual and damps it. The lower pane is residual z versus the fitted ẑ.

Math and metrics

Prefers chain.price.harmonicGap when available (≥40 pts); else in-browser fit. T=1460 days. Damping exp(−0.04·years from sample start).

z = log10(P/trend)/σ. ẑ = (b0 + b1 sin θ + b2 cos θ)·e^{−0.04 y}, θ=2π t / 1460.

damped fair = trend · 10^(ẑ σ).

Educational overlay. See Harmonic Fair Value for the gated walk-forward version.