Natural Frequency of Spring-Mass System

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-5

Evidence ID

t5-094

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json