#### 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 = d^{2}x/dt^{2} = -Aω^{2} cos(ωt + φ)

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

x_{max} = A

v_{max} = Aω

a_{max} = Aω^{2}

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

- The speed is maximum when the object passes through the equilibrium position (x = 0)
- The acceleration is opposite in direction, and proportional to, the displacement
- All three graphs have the same frequency - they just differ by phases of 90 degrees.