A $12-$N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y$($t$)=4\mathrm{.}50$ cm cos$[(19\mathrm{.}5$s$-1)$t$-$pie$/8].($a$)$ What is the spring constant of the spring? $($b$)$ what is its velocity when the object is at y $=2\mathrm{.}5$ cm below the equilibrium position going upwards? $($c$)$ How long does it take the object to go from its highest point to its lowest point?