Problem $14($Halliday Problem $15\mathrm{.}33)$

A block of mass $M=5\mathrm{.}4kg,$ at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant $k=6000\frac{N}{m}.$ A bullet of mass $m=9\mathrm{.}5g$ and velocity vec$(v)$ of magnitude $630\frac{m}{s}$ strikes and is embedded in the block $($Fig$.15-40).$ Assuming the compression of the spring is negligible until the bullet is embedded, determine $($a$)$ the speed of the block immediately after the collision and $($b$)$ the amplitude of the resulting simple harmonic motion.