Source: https://guthlabs.ai/docs/instruments/simple-pendulum-period-calculator/implementation/

instrument implementation / implementation-contract

# Simple Pendulum Period Calculator implementation

A source-bound implementation contract for Simple Pendulum Period Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-047

**Effect**: Computation or source lookup only

## Input and validation requirements

The specification exposes unsafe edge behavior unless the instrument rejects g=0 and nonphysical g values, and it has a significant angle-unit convention hazard. The small-angle branch also becomes inaccurate beyond approximately 15 degrees.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "L": 1,
    "L_unit": "m",
    "g": 9.81,
    "g_unit": "m/s^2",
    "theta0": 0,
    "angle_unit": "rad"
  },
  "expected_outputs": {
    "T_small_s": 2.00606668,
    "T_exact_s": 2.00606668,
    "exact_minus_small_s": 0,
    "K_modulus": 1.57079633,
    "small_to_exact_ratio": 1
  },
  "working": "sqrt(L/g)=sqrt(1/9.81)=0.3194382825. T_small=2π(0.3194382825)=6.283185307×0.3194382825=2.00606668 s. θ0=0, so k=sin(0/2)=0 and K(0)=π/2=1.570796327. T_exact=4(0.3194382825)(π/2)=2π(0.3194382825)=2.00606668 s. Difference=2.00606668−2.00606668=0."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/simple-pendulum-period-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/simple-pendulum-period-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/simple-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-tranche6/tranche6-results.json`