Mass-spring SHM API

Computes angular frequency ω=sqrt(k/m), period T=2π·sqrt(m/k), and frequency for a mass–spring oscillator, plus max velocity, acceleration, and energy for a given amplitude. Answers 'What is the period of a mass on a spring?', 'What is the natural frequency of an oscillator?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/simple-harmonic-motion

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsphysicsshmsimple-harmonic-motionoscillationnatural-frequencyperiod

API URLhttps://x402.hexl.dev/v1/engineering/simple-harmonic-motion

Integration docs

Example request

{
  "massKg": 0.5,
  "springConstantNm": 200,
  "amplitudeM": 0.05
}

Example response

{
  "massKg": 0.5,
  "springConstantNm": 200,
  "angularFrequencyRadS": 20,
  "periodS": 0.314159,
  "frequencyHz": 3.183099,
  "formula": "ω = sqrt(k/m), T = 2π*sqrt(m/k), f = 1/T",
  "amplitudeM": 0.05,
  "maxVelocityMs": 1,
  "maxAccelerationMs2": 20,
  "maxEnergyJ": 0.25
}

Input schema

{
  "type": "object",
  "required": [
    "massKg",
    "springConstantNm"
  ],
  "properties": {
    "massKg": {
      "type": "number",
      "description": "oscillating mass (kg)",
      "examples": [
        0.5
      ]
    },
    "springConstantNm": {
      "type": "number",
      "description": "spring constant k (N/m)"
    },
    "amplitudeM": {
      "type": "number",
      "description": "oscillation amplitude (m)"
    }
  }
}

Output schema

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