Simple pendulum period API

Computes the small-angle period T=2π·sqrt(L/g) and frequency of a simple pendulum, with an optional first-order large-amplitude correction. Answers 'What is the period of a pendulum?', 'How does amplitude affect the pendulum period?'.

Price$0.02per request

MethodPOST

Route/v1/engineering/pendulum-period

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsphysicspendulumperiodoscillationfrequencyharmonic

API URLhttps://x402.hexl.dev/v1/engineering/pendulum-period

Integration docs

Example request

{
  "lengthM": 1,
  "amplitudeDeg": 20
}

Example response

{
  "lengthM": 1,
  "gravityMs2": 9.80665,
  "periodS": 2.006409,
  "frequencyHz": 0.498403,
  "formula": "T = 2π*sqrt(L/g)",
  "amplitudeDeg": 20,
  "correctedPeriodS": 2.021689,
  "correctionFormula": "T ≈ T0*(1 + θ²/16)"
}

Input schema

{
  "type": "object",
  "required": [
    "lengthM"
  ],
  "properties": {
    "lengthM": {
      "type": "number",
      "description": "pendulum length (m)",
      "examples": [
        1
      ]
    },
    "gravity": {
      "type": "number",
      "description": "gravity (m/s^2), default 9.80665"
    },
    "amplitudeDeg": {
      "type": "number",
      "description": "swing amplitude (deg) for correction"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}