A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is $ x(t) = 8 \sin t, $ where $ t $ is in seconds and $ x $ in centimeters.
(a) Find the velocity and acceleration at time $ t. $
(b) Find the position, velocity, and acceleration of the mass at time $ t = 2\pi/3. $ In what direction is it moving at that time?