An object weighing $44\mathrm{.}1$ N hangs from a vertical massless ideal spring. When set in vertical

motion, the object obeys the equation y$($t$)=(6\mathrm{.}2$ cm$)$ cos$((2\mathrm{.}74$ rad$/$s$)$t $1\mathrm{.}4)$

a$)$ Find the time for this object to vibrate one complete cycle

b$)$ What is the total distance the object moves through in one cycle

c$)$ Find the maximum kinetic energy of the object

d$)$ What is the spring constant of the spring

$2$