Modelling motion · manipulative
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.
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
Formula sheet
At this instant