An oscillating block$-$spring system has a mechanical energy of $4\mathrm{.}10$ J$,$ an amplitude of $10\mathrm{.}1$ cm$,$ and a maximum speed of $1\mathrm{.}95$ m$/$s$.$ Find $($a$)$ the spring constant, $($b$)$ the mass of the block and $($c$)$ the frequency of oscillation.