By Zencalcy Editorial TeamLast reviewed About us
In simple harmonic motion the displacement follows a cosine curve when the object starts at maximum displacement. The amplitude sets how far it travels, and the angular frequency sets how quickly the cycle repeats.
Position in simple harmonic motion at a given time.
x = A cos(ω t)
x is displacement in metres, A the amplitude, ω the angular frequency in rad/s and t the time in seconds. This form assumes x = A at t = 0.
| Symbol | Meaning |
|---|---|
| x | Displacement from equilibrium, in metres. |
| A | Amplitude, in metres. |
| ω | Angular frequency, in rad/s. |
| t | Time, in seconds. |
The phase is 1 rad, so x = 0.1 × cos 1 = 0.054 m. The oscillator has moved just over half of its amplitude toward equilibrium.
Continue with the SHM Velocity Calculator, Simple Pendulum Calculator, or the Spring Period Calculator — or browse more rotational and periodic motion tools and all physics calculators.
Cosine is chosen because the motion starts at maximum displacement, where the velocity is zero. A sine form would describe starting at equilibrium instead.
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.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026