An oscillating block$-$spring system has a mechanical energy of $1\mathrm{.}30$ J$,$ an amplitude of $12\mathrm{.}7$ cm$,$ and a maximum speed of $3\mathrm{.}91$ m$/$s$.$ Find $($a$)$ the spring constant, $($b$)$ the mass of the block and $($c$)$ the frequency of oscillation.