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🎵 Simple Harmonic Motion Calculator

Calculate the displacement, velocity, and acceleration of an object undergoing simple harmonic motion at a given time.

1
m
2
rad/s
3
s

What simple harmonic motion is

Simple harmonic motion (SHM) describes a repetitive back-and-forth motion where the restoring force is proportional to displacement from equilibrium, such as a mass on a spring or a small-angle pendulum swing.

The formulas used

Assuming the object starts at maximum displacement, position at time t is x(t) = A·cos(ωt), velocity is v(t) = −Aω·sin(ωt), and acceleration is a(t) = −Aω²·cos(ωt), where A is amplitude and ω is angular frequency.

This model assumes an idealized SHM system with no damping or friction losses. For general physics education purposes.

Last reviewed August 2026