A rotating point casts a shadow that moves back and forth sinusoidally.
WHAT HAPPENS IF…Where is speed largest?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideax(t)=Acos(ωt),x′′=−ω2x
Differentiate twice: velocity is −Aω sin(ωt), and acceleration is −Aω²cos(ωt). Thus the restoring acceleration is proportional to displacement and points toward equilibrium. The period is 2π/ω for ω>0.
A detail that matters
Acceleration is not zero at a turning point, even though velocity is.