A $1\mathrm{.}5-$kg block attached to an ideal massless spring oscillates on a horizontal, frictionless track.

A force of $0\mathrm{.}5$ N is applied to stretch the spring by $10$ cm from its upstretched length.

$($a$)$ What is the spring stiffness constant?

$($b$)$ Find the period of the oscillations.

$($c$)$ Sketch the position of the block as a function of time. Clearly label the axes and period of the motion.