A horizontal block$-$spring system with the block on a frictionless surface has total mechanical energy E $=47\mathrm{.}0$

J and a maximum displacement from equilibrium of $0\mathrm{.}240$ m$.($a$)$ What is the spring constant? $($b$)$ What is the

kinetic energy of the system at the equilibrium point? $($c$)$ If the maximum speed of the block is $3\mathrm{.}45$ m$/$s$,$ what is

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

stored in the spring when x $=0\mathrm{.}160$ m$.($f$)$ Suppose the same system is released from rest at x $=0\mathrm{.}240$ m on a

rough surface so that it loses $14\mathrm{.}0$ J by the time it reaches its first turning point $($after passing equilibrium at x $=0).$

What is its position at that instant?