$[2/7$ Points$]$

SCALCET$93\mathrm{.}3\mathrm{.}041.$MI$.$

A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is $x(t)=4sin(t),$ where

$$

$($a$)$ Find the velocity and acceleration at time $t.$

$v(t)=$

$a(t)=$

$$

$$

$($b$)$ Find the position, velocity, and acceleration of the mass at time $t=2\frac{}{3}.$

$x(\frac{2}{3})=$

$x(\frac{2}{3})=$

$a(\frac{2}{3})=$

In what direction is the mass moving at that time?