Mass-Spring Period Calculator (SHM)
Find the oscillation period, frequency and angular frequency of a mass on a spring in simple harmonic motion.
How it works
ω = √(k ÷ m) · T = 2π·√(m ÷ k) · f = 1 ÷ T
A mass on an ideal spring undergoes simple harmonic motion with a period T = 2π√(m/k). A stiffer spring (larger k) shortens the period, while a heavier mass lengthens it — and because both appear under a square root, quadrupling the mass only doubles the period. Notice the amplitude does not appear: within the elastic limit a spring keeps the same period whether it swings a little or a lot, a property called isochronism.
Worked example
A 0.5 kg mass on a spring of k = 200 N/m: ω = √(200/0.5) = √400 = 20 rad/s. The period is T = 2π/20 ≈ 0.314 s and the frequency f = 1/0.314 ≈ 3.18 Hz.
Sources: Simple harmonic motion — Wikipedia
Frequently asked questions
Does the amplitude change the period?
No. For an ideal spring the period depends only on the mass and spring constant, not on how far you pull it. This amplitude-independence is what makes simple harmonic motion so useful for timekeeping.
How does gravity affect a vertical spring?
Gravity only shifts the equilibrium position downward; it does not change the period. A vertical mass-spring system oscillates about its new resting point with the same T = 2π√(m/k) as a horizontal one.
How is this different from a pendulum?
A pendulum’s period depends on its length and gravity (T = 2π√(L/g)), not its mass, while a mass-spring period depends on mass and stiffness. Both are simple harmonic, but the restoring forces come from different sources.
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This calculator is for educational purposes. Double-check important results before acting on them.