🪀 Spring Oscillation Calculator
Enter the mass and spring stiffness to get the oscillation period, frequency and angular frequency.
Period
0.314 s
Frequency
3.18 Hz
Angular ω
20 rad/s
A mass on a spring oscillates with period T = 2π·√(m/k), where m is the mass and k the spring stiffness. A heavier mass or a softer spring gives a slower oscillation; the angular frequency is ω = √(k/m) = 2πf. Gravity doesn\'t affect the period — it only shifts the equilibrium point. This assumes an ideal, massless spring and no damping. 🔒 In your browser.
How the spring oscillation calculator works
A mass bouncing on an ideal spring undergoes simple harmonic motion with period T = 2π·√(m/k), where m is the mass and k the spring constant (stiffness). A heavier mass or a softer spring oscillates more slowly. From the period you get the frequency f = 1/T (oscillations per second) and the angular frequency ω = √(k/m) = 2πf. Gravity plays no part in the period — it only shifts where the mass hangs at rest.
This assumes an ideal massless spring obeying Hooke's law and no damping or friction, so a real spring-mass system runs slightly differently and eventually decays. The spring constant k comes from the spring itself (force ÷ stretch, in N/m); measure it by hanging a known weight and seeing how far the spring extends.
Frequently asked questions
How do you calculate the period of a spring?
T = 2π·√(m/k), where m is the mass in kilograms and k the spring constant in newtons per metre. A 0.5 kg mass on a 200 N/m spring has a period of about 0.31 seconds.
Does gravity affect a spring's oscillation period?
No. Gravity only changes the equilibrium position the mass hangs at; the period depends solely on mass and spring stiffness. A vertical and a horizontal spring-mass system oscillate at the same rate.
What is the spring constant k?
A measure of a spring's stiffness — the force needed per unit of stretch, in newtons per metre (Hooke's law, F = kx). A stiffer spring has a higher k and, for the same mass, oscillates faster.
What is angular frequency?
ω = √(k/m) = 2πf, in radians per second. It's the natural rate of the oscillation used in the equations of motion; the ordinary frequency f = ω/2π counts full cycles per second.
How does mass change the oscillation?
A heavier mass oscillates more slowly: the period grows with the square root of mass, so quadrupling the mass doubles the period. A lighter mass on the same spring bounces faster.