🪀 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.