Read the equation
The function returns −ω²x, the acceleration term of a harmonic oscillator with displacement x. It does not evaluate the full displayed residual ∂²x/∂t²+ω²x, which would vanish for an exact oscillator solution. No temporal differentiation or spatial wave propagation is performed inside this helper.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| omega | Declared frequency |
| x | Displacement-like scalar |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
wk := 1.0 / float64(k) // Weight decreases with distance
xk := math.Sin(float64(k) * x)
sum += wk * xk
}
return sum
}
// FPoseidon: F_Poseidon(x) = ∂²x/∂t² + ω²x (Depth/Emotion - wave equation)
func FPoseidon(x float64) float64 {
// Solution to wave equation: A·cos(ωt)
omega := 2.0 * math.Pi / BasePairsPerTurn
return -omega * omega * x // ∂²x/∂t² term
}
// FDemeter: F_Demeter(x) = x·(1-x/K) (Growth - logistic growth)
func FDemeter(x float64) float64 {
K := 1.0 // Carrying capacity
r := 0.5 // Growth rateExact original notation
FPoseidon: F_Poseidon(x) = ∂²x/∂t² + ω²x (Depth/Emotion - wave equation)