Modelling motion · manipulative

Simple harmonic motion

If d²x/dt² = −ω²x, then x = A cos(ωt + β). Watch x, v and a over time — and how v and a sit against displacement x.

x v a

Against time · x(t), v(t), a(t)

Against displacement · v(x) and a(x)

Ellipse v² = ω²(A² − x²) · line a = −ω²x

Pause, then drag the mass or the time graph to set position · Play to run · Swap graphs to put either plot on top

Amplitude and angular frequency

2.0
1.5
Period T = 2π/ω
Frequency f = 1/T

Formula sheet

At this instant