Natural Frequency of Spring-Mass System mechanism

Model scope

The core frequency formulas are correct under standard SI and undamped SDOF assumptions, but the specification needs review because Tn lacks an explicit formula, the static pathway does not specify g or its default, and unit conventions are not defined. The empty honest_label is a concern: the instrument should clearly state that it computes idealized undamped natural frequency and period, not damped or experimentally measured frequency, and should disclose the required SI-unit conversions and static-deflection assumptions.

• ωn=√(k/m) and fn=ωn/(2π) are standard for an undamped single-degree-of-freedom spring-mass system, assuming k is the effective linear stiffness and m is the effective mass.
• Tn is listed as an output but its formula is omitted; it must be explicitly defined as Tn=2π/ωn=1/fn.
• δst=mg/k and fn=(1/(2π))√(g/δst) are valid only when δst is the static displacement caused by the mass's weight in a vertical linear spring system, with no relevant preload or geometric complication.
• The static-deflection pathway requires a specified gravitational acceleration g, but g is not listed as an input or default.

Units and conventions

• For ωn=√(k/m), use k in N/m and m in kg, producing ωn in rad/s.
• fn is in Hz (cycles/s), and Tn is in seconds.
• For the static-deflection formula, δst must be in meters and g in m/s²; standard Earth gravity g=9.81 m/s² is assumed only when explicitly stated.
• Radians are dimensionless in the numerical calculations, but ωn should still be labeled rad/s.
• Any stiffness entered in N/mm must be converted to N/m before applying the formula.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "stiffness_mass",
    "k": 900,
    "k_unit": "N/m",
    "m": 4,
    "m_unit": "kg"
  },
  "expected_outputs": {
    "omega_n": 15,
    "omega_n_unit": "rad/s",
    "f_n": 2.387324146,
    "f_n_unit": "Hz",
    "T_n": 0.41887902,
    "T_n_unit": "s"
  },
  "working": "ωn=√(k/m)=√(900/4)=√225=15 rad/s. fn=ωn/(2π)=15/6.283185307=2.387324146 Hz. Tn=2π/ωn=6.283185307/15=0.41887902 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The boundary and zero-mass vectors require explicit rejection or special handling, and the signed static-deflection vector exposes a convention-dependent domain failure. The formula-branch comparison is internally consistent for valid positive inputs.

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-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json