Physical (Compound) Pendulum Period Calculator mechanism

Model scope

The formula is correct for an ideal undamped rigid compound pendulum in the small-angle limit. The existing honest label is appropriate. Verdict is NEEDS_REVIEW because the input units and treatment of gravitational acceleration g are not explicitly specified.

• The formula T=2π√(I/(mgd)) is the standard small-angle period for an ideal rigid compound pendulum when I is the mass moment of inertia about the pivot and d is the pivot-to-center-of-mass distance.
• The specification does not state whether g is a fixed constant or an omitted input; the assumed value must be disclosed.
• The specification does not state domain constraints: m>0, I>0, d>0, and a stable equilibrium configuration are required for a finite real period.

Units and conventions

• Use SI units: I in kg·m², m in kg, d in m, g in m/s², and T in seconds.
• Assume standard gravitational acceleration g=9.81 m/s² unless the instrument explicitly exposes another value.
• I must be the total mass moment of inertia about the actual pivot axis, not about the center of mass.
• d is the positive distance from the pivot to the center of mass.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "I": 1,
    "m": 2,
    "d": 0.5
  },
  "expected_outputs": {
    "T": 2.006067
  },
  "working": "g=9.81 m/s². mgd=2×9.81×0.5=9.81. I/(mgd)=1.0/9.81=0.101936799. √(I/(mgd))=√0.101936799=0.319275428 s. T=2π×0.319275428=6.283185307×0.319275428=2.006067 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Inputs with d = 0 produce a zero denominator and are undefined, while a negative signed d produces a non-real square-root argument if interpreted literally. The supplied specification does not state input validation or an absolute-value convention.

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