Graphs of position, velocity, and acceleration

In SHM, the general equations for position, velocity, and acceleration are:

x(t) = A cos(ωt + φ)

v = dx/dt = -Aω sin(ωt + φ)

a = d2x/dt2 = -Aω2 cos(ωt + φ)

Whatever is multiplying the sine or cosine represents the maximum value of the quantity. Thus:

xmax = A

vmax = Aω

amax = Aω2

Angular frequency:

Graphing the position, velocity, and acceleration allows us to see some of the general features of simple harmonic motion: