A bullet with mass $m=10\mathrm{.}0$g bullet is fired into a block with mass $m=2\mathrm{.}20$kg which is attached to a spring with a force constant of $23\mathrm{.}N/m.$ The bullet has a speed of $300$m/s just before it strikes the block and the block slides on a frictionless surface. Find how far the spring is compressed in units of cm.

After the spring is compressed, the system undergoes simple harmonic motion. Find the magnitude of the velocity when the block $($with embedded bullet$)$ is a half$-$way through a full amplitude.