Physics

Mass–spring period

Find period, mass or spring constant for an ideal oscillator.

Your measurements

Number formats & units

Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.

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Result & working

Example

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Formula & example

The relationship

T=2\pi\sqrt{\frac mk}

k=\frac{4\pi^2m}{T^2}

m=k\left(\frac{T}{2\pi}\right)^2

What the variables mean

Symbol	Meaning
$T$	Oscillation period in seconds.
$m$	Oscillating mass in kilograms.
$k$	Spring constant in N m⁻¹.

Worked example

Solve for: Period T
Mass m (kg): 0.250
Spring constant k (N/m): 10

0.9934588 s

Follow the example steps

T = 2π√(m/k)
= 2π√(0.25 / 10) = 0.9934588 s

Common mistakes

Use kilograms in the SI mass–spring equation.

Incorrect approach

m = 100 g, k = 10 N/m: T = 2π√(100/10)

Correct approach

m = 0.1 kg: T = 2π√(0.1/10) ≈ 0.6283 s

More checks before you submit

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.

Method notes

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.

Mass–spring period

Your measurements

Result & working

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Formula & example

The relationship

Worked example

Common mistakes

✕ Incorrect approach

✓ Correct approach

Linear regression

Repeated measurements & timing

Physical constants from gradients

Incorrect approach

Correct approach