A mass attached to a vertical spring has position function given by y(t) = A sin wt,

Question:

A mass attached to a vertical spring has position function given by y(t) = A sin wt, where A is the amplitude of its oscillations and is a constant.
(a) Find the velocity and acceleration as functions of time.
(b) Show that the acceleration is proportional to the displacement y.
(c) Show that the speed is a maximum when the acceleration is 0.