A spring with spring constant k $=3000$ N$/$m is oriented vertically and an object of mass $0\mathrm{.}50$ kg is

dropped from rest at a height of $3\mathrm{.}0$ m onto the spring.

a$)$ Using conservation of energy determine the speed with which the mass will strike the spring

Determine how far the spring will compress. Let all motion be along the y$-$axis and take the

equilibrium position of the spring to be the origin of your coordinate system $($Hint: When you

do this, at the point of maximum compression the spring will have NEGATIVE mgy potential

energy in addition to the potential energy of the compressed spring