A $4\mathrm{.}32$ kg object on a horizontal frictionless surface is attached to a spring with $k=1870\frac{N}{m}.$ The object is displaced from equilibrium $42\mathrm{.}1$ cm horizontally and given an initial velocity of $14\mathrm{.}4\frac{m}{s}$ back toward the equilibrium position. What are $($a$)$ the motion's frequency, $($b$)$ the initial potential energy of the block$-$spring system, $($c$)$ the initial kinetic energy, and $($d$)$ the motion's amplitude?

$($a$)$ Number

Units

$($b$)$ Number

Units

$($c$)$ Number

Units

$($d$)$ Number

Units