Music Box — x(t) = Σ Aₙe^{-γₙt}sin(nωt)Tap to zoom

Music Box

x(t) = Σ Aₙe^{-γₙt}sin(nωt)

Harmonic overtones decaying at different rates — the higher notes fade first, leaving only the fundamental.

The melody simplifying as the mechanism slows

Part of: NOSTALGIA

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Carousel — r(t) = R · e^{iωt}, ω → 0

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r(t) = R · e^{iωt}, ω → 0

Daguerreotype — I(x,y,t) = I₀(x,y) · e^{-t/τ} + η(x,y)

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I(x,y,t) = I₀(x,y) · e^{-t/τ} + η(x,y)

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f(x) = f₀(x) * g(σ), σ → ∞

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R(x) = lim_{t→∞} f(x,t)