Source: https://guthlabs.ai/docs/instruments/physical-compound-pendulum-period-calculator/mechanism/

instrument mechanism / verified-clean

# Physical (Compound) Pendulum Period Calculator mechanism

The inspectable method record for Physical (Compound) Pendulum Period Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/physical-compound-pendulum-period-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/physical-compound-pendulum-period-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/physical-compound-pendulum-period-calculator/qualification/>)

## 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`