An oscillating block$-$spring system has a mechanical energy of $2\mathrm{.}43$ J $,$ an amplitude of $13\mathrm{.}7$ cm $,$ and a maximum speed of $\backslash (3\mathrm{.}42\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Find $($a$)$ the spring constant, $($b$)$ the mass of the block and $($c$)$ the frequency of oscillation.