An oscillating block$-$spring system has a mechanical energy of $2\mathrm{.}73$ J$,$ an amplitude of $9\mathrm{.}82$ cm$,$ and a maximum speed of $1\mathrm{.}91$ m$/$s$.$ Find

$($a$)$ the spring constant, $($b$)$ the mass of the block and $($c$)$ the frequency of oscillation.