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An oscillating block$-$spring system has a mechanical energy of $4\mathrm{.}73$ J $,$ an amplitude of $9\mathrm{.}89$ cm $,$ and a maximum speed of $1\mathrm{.}57\frac{m}{s}.$ Find $($a$)$ the spring constant, $($b$)$ the mass of the block and $($c$)$ the frequency of oscillation.