A $0\mathrm{.}10-$kg block oscillates back and forth along a straight line on a frictionless horizontal

surface. Its displacement from the origin is given by x$($t$)=(0\mathrm{.}10$ m$)$ cos$[(10$ rad$/$s$)$t$+$$/2$ rad$].$

$($a$)$ What is the oscillation frequency?

$($b$)$ What is the maximum speed acquired by the block?

$($c$)$ At what value of x does this occur?

$($d$)$ What is the magnitude of the maximum acceleration?

$($e$)$ At what value of x does this occur?

$($f$)$ What force, applied to the block by the spring, results in the given oscillation?