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Mass–Spring Natural Frequency Calculator — result sheet
Calculate angular frequency, frequency, and period for an ideal undamped mass–spring oscillator.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: ωₙ = √(k/m); fₙ = ωₙ/(2π); T = 2π√(m/k).
The ideal simple-harmonic model uses only mass and spring stiffness to return angular frequency, cycles per second, and period.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mass — kg; minimum 1.0E-6; maximum 1000000000
- Spring stiffness k — N/m; minimum 1.0E-6; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Mass | 2 |
| Spring stiffness k | 500 |
Natural angular frequency is 15.81 rad/s, frequency is 2.52 Hz, and period is 0.397 s.
Assumptions and limits
- The oscillator is linear, undamped, and small enough that the entered stiffness remains constant.
- The mass is the effective moving mass and mounting compliance, damping, friction, preload, and amplitude-dependent stiffness are not modeled.
- The result is a model natural frequency, not a vibration test or structural resonance certification.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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