What is the period of a mass on a spring?

T = 2π√(m/k). A heavier mass or a softer spring gives slower oscillations; the amplitude does not change the period.

The force from a spring is proportional to its extension, F = kx, as long as it is not stretched past its limit of proportionality. k is the spring constant in N/m.

What does damping do?

Damping removes energy every cycle, so the amplitude shrinks exponentially. Light damping barely changes the period; heavy damping can stop the oscillation altogether.

How do I find the spring constant from the period?

Rearrange T = 2π√(m/k) to k = 4π²m/T². A 0.50 kg mass bouncing with a period of 0.80 s gives k = 4π² × 0.50 / 0.80² = 30.8 N/m. Pick Spring constant under Solve for to see each step, or k from a stretch to use Hooke's law instead.

← All simulations

Mass on a spring

Simple harmonic motion: stiffness and mass set the period, damping drains the amplitude.

Just need the number? Physics Formulas

Displacement vs time

Readouts

What's happening

The spring pulls back with force −kx, so acceleration is proportional to displacement and points toward equilibrium, which is the definition of simple harmonic motion. The period 2π√(m/k) does not depend on the amplitude. Damping removes energy each cycle, shrinking the oscillation exponentially without changing its period much.

T = 2π √(m / k)F = −kx

GCSE Physics (AQA 4.5.3): Hooke's law F = kx. A-Level Physics (AQA 3.6.2): simple harmonic motion, damping and resonance.

Challenge

Predict first: if you quadruple the mass, what happens to the period? Run it at m and 4m and compare the graphs.

FAQ

What is the period of a mass on a spring?: T = 2π√(m/k). A heavier mass or a softer spring gives slower oscillations; the amplitude does not change the period.
What is Hooke's law?: The force from a spring is proportional to its extension, F = kx, as long as it is not stretched past its limit of proportionality. k is the spring constant in N/m.
What does damping do?: Damping removes energy every cycle, so the amplitude shrinks exponentially. Light damping barely changes the period; heavy damping can stop the oscillation altogether.
How do I find the spring constant from the period?: Rearrange T = 2π√(m/k) to k = 4π²m/T². A 0.50 kg mass bouncing with a period of 0.80 s gives k = 4π² × 0.50 / 0.80² = 30.8 N/m. Pick Spring constant under Solve for to see each step, or k from a stretch to use Hooke's law instead.