Driven Oscillator / Resonance Curve Calculator mechanism

Model scope

The amplitude expression itself is standard under the stated linear viscous-damping assumptions, but the instrument claims phase, resonance frequency, and Q outputs without defining their formulas or conventions. Because those omissions affect correctness and the existing honest_label is n/a while already_built is false, this specification requires correction before release.

• The amplitude formula is standard for a linear single-degree-of-freedom oscillator with viscous damping, provided ω0=√(k/m) and ζ=c/(2√(km)); these definitions are not supplied.
• The specification claims phase output but provides no phase formula. For displacement response convention x(t)=A cos(ωt−φ), the standard phase is φ=atan2(2ζω0ω,ω0²−ω²).
• The resonance-frequency formula is missing. For displacement amplitude and 0≤ζ<1/√2, ω_res=ω0√(1−2ζ²); for ζ≥1/√2, the amplitude maximum is at zero frequency rather than a positive-frequency resonance peak.
• The Q-factor formula is missing. For viscous damping, Q=1/(2ζ)=mω0/c, subject to positive k, m, and c.
• The formula assumes a linear oscillator, positive mass and stiffness, nonnegative viscous damping, and steady-state sinusoidal forcing. These constraints are not stated.

Units and conventions

• k is in N/m, m in kg, c in N·s/m, and F0 in N.
• ω and ω0 are angular frequencies in rad/s; if the sweep input is in Hz, convert using ω=2πf before evaluating the formula.
• Amplitude is displacement amplitude in meters.
• ζ is dimensionless, with ζ=c/(2√(km)).
• Phase is interpreted as the positive displacement lag φ in radians, using x(t)=A cos(ωt−φ).
• Q is dimensionless.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "k_N_per_m": 100,
    "m_kg": 1,
    "c_Ns_per_m": 2,
    "F0_N": 1,
    "sampled_frequency": {
      "omega_rad_per_s": 0
    },
    "sweep": {
      "omega_min_rad_per_s": 0,
      "omega_max_rad_per_s": 20
    }
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "omega_rad_per_s": 0,
        "amplitude_m": 0.01,
        "phase_rad": 0
      }
    ],
    "resonance_frequency_rad_per_s": 9.89949493661,
    "resonance_frequency_hz": 1.5755535327,
    "peak_amplitude_m": 0.05025189076296,
    "Q": 5
  },
  "working": "ω0=√(k/m)=√(100/1)=10 rad/s. ζ=c/(2√(km))=2/(2√(100·1))=2/20=0.1. At ω=0: denominator=√((10²−0²)²+(2·0.1·10·0)²)=√(10000)=100. A=(F0/m)/denominator=(1/1)/100=0.01 m. φ=atan2(0,100)=0 rad. ωres=10√(1−2·0.1²)=10√(0.98)=9.89949493661 rad/s. At the peak, denominator=2ζω0²√(1−ζ²)=2·0.1·10²·√(0.99)=19.8997487421, so Apeak=1/19.8997487421=0.050251890763 m. Q=1/(2ζ)=1/0.2=5."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument specification permits m=0 as an input unless validation prevents it, but m=0 makes both F0/m and omega0=sqrt(k/m) undefined. The resonance branch also requires explicit handling at zeta=1/sqrt(2) and above, where the nonzero resonance-frequency formula otherwise produces an imaginary result.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json