horizontal block$-$spring system with the block on a frictionless surface has total mechanical energy E $=44\mathrm{.}1$ J and a maximum displacement from equilibrium of $0\mathrm{.}235$ m$.$

$($a$)$ What is the spring constant?

N$/$m

$($b$)$ What is the kinetic energy of the system at the equilibrium point?

J

$($c$)$ If the maximum speed of the block is $3\mathrm{.}45$ m$/$s$,$ what is its mass?

kg

$($d$)$ What is the speed of the block when its displacement is $0\mathrm{.}160$ m$?$

m$/$s

$($e$)$ Find the kinetic energy of the block at x $=0\mathrm{.}160$ m$.$

J

$($f$)$ Find the potential energy stored in the spring when x $=0\mathrm{.}160$ m$.$

J

$($g$)$ Suppose the same system is released from rest at x $=0\mathrm{.}235$ m on a rough surface so that it loses $16\mathrm{.}3$ J by the time it reaches its first turning point $($after passing equilibrium at x $=0).$ What is its position at that instant?

m