A mass of $0\mathrm{.}220$ 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$)=(0\mathrm{.}680$ m$)$cos$[(12\mathrm{.}0$ rad$/$s$)$t$].$

Determine the following.

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

$0\mathrm{.}680$

Correct: Your answer is correct.

m

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

$31\mathrm{.}68$

Correct: Your answer is correct.

N$/$m

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

$-0\mathrm{.}680$

Correct: Your answer is correct.

m

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

$0\mathrm{.}340$

Correct: Your answer is correct.

m

$($e$)$ time it takes the mass to get to the position

x $=0\mathrm{.}500$ m

after it has been released