A $180-$g block is pressed against a spring of force constant $1\mathrm{.}15$ kN$/$m until the block compresses the spring $10\mathrm{.}0$ cm$.$ The spring rests at the bottom of a ramp inclined at $60\mathrm{.}0$ to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops under the following conditions.

$($a$)$ if the ramp exerts no friction force on the block

m

$($b$)$ if the coefficient of kinetic friction is $0\mathrm{.}440$

m