b$)$ A $2$ kg block is supported as shown by a spring of constant $\backslash ($ k$=400\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ),$ which can act in tension or compression. The block is in its equilibrium position when it is struck from below by a hammer, which imparts to the block an upward velocity of $\backslash (2\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Determine $(\backslash ($ a $\backslash ))$ the time required for the block to move $100$ mm upward, $($b$)$ the corresponding velocity and acceleration of the block.