Physics
Mass–Spring Period Calculator
Use the small-amplitude simple-harmonic model for a mass on an ideal spring.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
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Step-by-step working
The formula
T = 2π√(m/k)
k = 4π²m/T²
m = k(T/2π)²
| Symbol | Meaning |
|---|---|
| T | Oscillation period in seconds. |
| m | Oscillating mass in kilograms. |
| k | Spring constant in N m⁻¹. |
When to use this calculator
Use this for an ideal horizontal mass–spring system, or for vertical oscillations about equilibrium when the spring remains in its linear range.
For real springs, the spring’s own effective mass, damping and non-linear behaviour can shift the period. Measure several oscillations for a more precise experimental period.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- T = 2π√(m/k)
- = 2π√(0.25 / 10) = 0.9934588 s
0.9934588 s
Common mistakes
- Use kilograms, not grams, in the SI form.
- The static extension mg/k is not the oscillation amplitude.
- Do not assume Hooke’s law remains valid beyond the spring’s linear range.