A particle executes linear SHM with frequency $0\mathrm{.}51$ Hz about the point x $=0.$ At t $=0,$ it has displacement x $=0\mathrm{.}66$ cm and zero velocity. Determine the following values for the motion.

$($a$)$ the period

s

$($b$)$ the angular frequency

rad$/$s

$($c$)$ the amplitude

cm

$($d$)$ the displacement x$($t$)($Use the following as necessary: t$.$ Assume t is in seconds.$)$

x$($t$)=$

$0\mathrm{.}66$cos$($t$)$

cm

$($e$)$ the velocity v$($t$)($Use the following as necessary: t$.$ Assume t is in seconds.$)$

v$($t$)=$

$2\mathrm{.}115$sin$($t$)$

cm$/$s

$($f$)$ the maximum speed

cm$/$s

$($g$)$ the magnitude of the maximum acceleration

cm$/$s$2$

$($h$)$ the displacement at t $=3\mathrm{.}0$ s

cm

$($i$)$ the speed at t $=3\mathrm{.}0$ s

cm$/$s