A $4\mathrm{.}0$ kg block is suspended from a spring with $k=407\frac{N}{m}.$ A $54$ g bullet is fired into the block from directly below with a speed of $100\frac{m}{s}$ and becomes embedded in the block. $($a$)$ Find the amplitude of the resulting simple harmonic motion. $($b$)$ What percentage of the original kinetic energy of the bullet is transferred to mechanical energy of the harmonic oscillator?

$($a$)$ Number $$ Units $$

$($b$)$ Number $$ Units $$