Once you know the position of the oscillator for all times, you can work out the velocity and acceleration functions.

- x(t) = A cos (wt
+ f)

The velocity is the time derivative of the position so:

v(t) = -A w sin (wt + f)

The change from cos to sin means that the velocity is 90

The acceleration is the time derivative of the velocity so:

a(t) = -A w

Notice also from the preceding that:

a(t) = -w