A $12\mathrm{.}0$N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as function of time t is given by y$($t$)=4\mathrm{.}50$cm cos$[(19\mathrm{.}5$s$^-1)$t$-$pi$/8].$

$($a$)$ What is the spring consrtant of the spring?

$($b$)$ What is the maximum acceleration of the object?

$($c$)$ what is the maximum speed that the object reaches?

$($d$)$ how long does it take the object to go from its highest point to its lowest point?