$12\mathrm{.}16)$ A block$-$spring system oscillates with an amplitude of $3\mathrm{.}50$ cm$.$ The spring constant is $250$ N$/$m and the mass of the block is $0\mathrm{.}500$ kg$.$ Determine $($a$)$ the mechanical energy of the system, $($b$)$ the maximum speed of the block, and $($c$)$ the maximum acceleration.