A horizontal block$-$spring system with the block on a frictionless surface has total mechanical energy $\backslash ($ E$=55\mathrm{.}1\backslash$mathrm$\{$~J$\}\backslash )$ and a maximum displacement from equilibrium of $0\mathrm{.}229$ m$.$

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

$-\backslash (\backslash$mathrm$\{$N$\}/\backslash$mathrm$\{$m$\}\backslash )$

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

$55$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$J$\}\backslash )$

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

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$kg$\}\backslash )$

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

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )$

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

Your response is within $\backslash (10\backslash \%\backslash )$ of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four$-$digit accuracy to minimize roundoff error. J

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

Your response is within $\backslash (10\backslash \%\backslash )$ of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four$-$digit accuracy to minimize roundoff error. J

$($g$)$ Suppose the same system is released from rest at $\backslash ($ x$=0\mathrm{.}229\backslash$mathrm$\{$~m$\}\backslash )$ on a rough surface so that it loses $15\mathrm{.}1$ J by the time it reaches its first turning point $($after passing equilibrium at $\backslash ($ x$=0\backslash )).$ What is its position at that instant?