Solve simple harmonic motion: angular frequency, period, peak velocity, acceleration and energy.
Solve simple harmonic motion: angular frequency, period, peak velocity, acceleration and energy.
Frequency (Hz)
How to use this tool
Mass attached to the spring, in kilograms.
Stiffness k in newtons per metre; stiffer springs oscillate faster.
Maximum displacement from equilibrium, in metres.
Frequency is independent of amplitude for ideal SHM; energy grows with amplitude squared.
Formula & worked example
Mass 1 kg, k = 100 N/m, amplitude 0.1 m: ω = 10 rad/s, f = 1.5915 Hz, T = 0.6283 s, v_max = 1 m/s, a_max = 10 m/s², energy 0.5 J.
Limitations — read this before you rely on it
This is undamped, ideal simple harmonic motion with a massless, linear spring. Real systems lose energy to damping and friction, and springs become non-linear at large extensions.
Frequently asked questions
No — for ideal SHM the period depends only on mass and spring constant, not amplitude.
ω in radians per second; ordinary frequency in hertz is ω divided by 2π.
At equilibrium, where displacement is zero; velocity is zero at the turning points.
At the turning points, where the spring force is largest; acceleration is zero at equilibrium.
Total energy stays constant, swapping between kinetic energy (maximum at equilibrium) and spring potential energy (maximum at the extremes).