By Zencalcy Editorial TeamLast reviewed About us
In simple harmonic motion acceleration always points back toward equilibrium and is proportional to displacement. It is greatest at the turning points, where the restoring force is strongest, and zero as the object passes through the centre.
Acceleration of a harmonic oscillator at time t.
a = −A ω² cos(ω t) = −ω² x
a is acceleration in m/s², A the amplitude, ω the angular frequency and x the displacement. The negative sign shows that acceleration opposes displacement.
| Symbol | Meaning |
|---|---|
| a | Acceleration, in m/s². |
| A | Amplitude, in metres. |
| ω | Angular frequency, in rad/s. |
| x | Displacement at that instant, in metres. |
The displacement is 0.054 m, so a = −ω²x = −4 × 0.054 = −0.216 m/s². The negative sign means the acceleration points toward equilibrium.
Continue with the SHM Displacement Calculator, SHM Velocity Calculator, or the Simple Pendulum Calculator — or browse more rotational and periodic motion tools and all physics calculators.
The restoring force always pulls the object back toward equilibrium. That is the defining feature of simple harmonic motion.
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