Numerical simulation, Runge-Kutta, RK4, harmonic o

ORCID: 0009-0002-6027-8680

Related Works: 10.5281/zenodo.22249411

Date: 7 September 2026

Core Constants:

√17 = 4.1231056, κ = √17/(100π) = 0.01312488

ω₀ = 2π/√17 ≈ 1.524 rad/s

F₀ = 412.31 Hz

Equations of Motion:

dx/dt = v

dv/dt = −ω₀²·x + κ·√17·sin(√17·t)

Method: 4th-order Runge-Kutta (RK4), dt = 0.1

Python Code:

import numpy as np

sqrt17 = np.sqrt(17)

kappa = sqrt17 / (100 * np.pi)

def deriv(t, y):

    x, v = y

    omega = 2 * np.pi / sqrt17

    return np.array([v, -omega**2 * x + kappa*sqrt17*np.sin(sqrt17*t)])

dt = 0.1

y = np.array([sqrt17, 0.0])

for step in range(1000):

    k1 = deriv(step*dt, y)

    k2 = deriv(step*dt+dt/2, y + dt/2*k1)

    k3 = deriv(step*dt+dt/2, y + dt/2*k2)

    k4 = deriv(step*dt+dt, y + dt*k3)

    y += dt/6 * (k1 + 2*k2 + 2*k3 + k4)

Results:

• Stable oscillation — no divergence

• Resonance builds over time

• Phase shift consistent with retrocausal term

• Full code available — open for independent verification