By Zencalcy Editorial TeamLast reviewed About us
The velocity of a simple harmonic oscillator peaks as it passes through equilibrium and falls to zero at the turning points. Its magnitude is Aω at most, and its sign tells you which way the object is moving.
Velocity of a simple harmonic oscillator at time t.
v = −A ω sin(ω t)
v is velocity in m/s, A the amplitude, ω the angular frequency and t the time. The maximum speed is Aω at the equilibrium point.
| Symbol | Meaning |
|---|---|
| v | Velocity, in m/s; negative means opposite the positive direction. |
| A | Amplitude, in metres. |
| ω | Angular frequency, in rad/s. |
| t | Time, in seconds. |
v = −0.1 × 2 × sin 1 = −0.168 m/s. The oscillator is heading back toward equilibrium, which is the negative direction for this starting phase.
Continue with the Simple Pendulum Calculator, Spring Period Calculator, or the Angular Acceleration Calculator — or browse more rotational and periodic motion tools and all physics calculators.
At the equilibrium position, where all the energy is kinetic. There the speed equals Aω.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026