IMPORTANT NOTE: This cannot be solved using $.$

A mass of $0\mathrm{.}38$ kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x$($t$)=(0\mathrm{.}28$m$)$cos$[(20$rad$//$s$)$t$].$ Determine the following.

$($a$)$ amplitude of oscillation for the oscillating mass

I

m

$($b$)$ force constant for the spring

$|$ N$/$m

$($c$)$ position of the mass after it has been oscillating for one half a period

m

$($d$)$ position of the mass one$-$third of a period after it has been released

$|$ m

$($e$)$ time it takes the mass to get to the position x$=-0\mathrm{.}10$m after it has been released

s