🎵 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