Interactive Simulator · Oscillations

Simple harmonic motion

In simple harmonic motion the acceleration is always proportional to the displacement and directed back toward the equilibrium position: a = −ω²x. The result is a sine-shaped oscillation. Watch the displacement, velocity and acceleration trace out their curves and notice how they line up.

Mission Predict how the acceleration of an object in SHM relates to its displacement. Streak 0Best 0
In simple harmonic motion the acceleration is:
angular frequency ω = 2π / T3.14 rad s⁻¹
frequency f = 1 / T0.50 Hz
displacement x = x₀ sin ωt0.0 cm
Blue: displacement. Green: velocity, a quarter cycle ahead. Orange: acceleration, exactly opposite the displacement, a = −ω²x.