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Simple Pendulum Frequency — result sheet
Estimate the oscillation frequency of an ideal simple pendulum from its length and local gravity.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Frequency f = sqrt(g/L) / (2 pi).
For small angular displacements, a simple pendulum behaves approximately like a harmonic oscillator. The frequency depends on length and gravity, not bob mass in this ideal model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Pendulum length — m; minimum 1.0E-6; maximum 1000000
- Gravitational acceleration — m/s^2; minimum 1.0E-6; maximum 100
Worked example
| Input | Value |
|---|---|
| Pendulum length | 1 |
| Gravitational acceleration | 9.80665 |
Frequency is about 0.4985 Hz.
Assumptions and limits
- The angle is small enough for the small-angle approximation.
- The string or rod is massless and the pivot is frictionless.
- Air drag, amplitude dependence, string stretch, and finite bob size are not modeled.
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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