$1.$ You stand on a bathroom scale, the spring inside the scale compresses $5\mathrm{.}00$ mm $,$ and it reads your weight as $600$ N $.$

a$.$ Determine the spring constant, k$.$ Create a relevant FBD$.$

b$.$ If you fall from rest onto the scale from a height of $0\mathrm{.}100$ m $,$ what does the scale read at its peak? Sketch the initial and final conditions of your system, indicating what form$($s$)$ of energy are present in each state.