By Zencalcy Editorial TeamLast reviewed About us
A mass on an ideal spring oscillates with a period set by the mass and the spring constant. A stiffer spring shortens the period; a heavier mass lengthens it, and the period is independent of amplitude within the spring's elastic limit.
Oscillation period of a mass on a spring.
T = 2π √(m / k)
T is the period in seconds, m the oscillating mass in kilograms and k the spring constant in N/m. The mass of the spring itself is ignored.
| Symbol | Meaning |
|---|---|
| T | Period of oscillation, in seconds. |
| m | Oscillating mass, in kilograms. |
| k | Spring constant, in N/m. |
T = 2π√(1 / 100) = 0.628 s, a frequency of 1.59 Hz. Doubling the mass stretches the period to 0.889 s.
Continue with the Angular Acceleration Calculator, Angular Momentum Calculator, or the Angular Velocity Calculator — or browse more rotational and periodic motion tools and all physics calculators.
No. Gravity shifts the equilibrium position but does not change the oscillation period of a mass-spring system.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026