Part $($a$)$ Using the given information, determine the

spring constant, k$,$ in Newtons per meter, of the

spring.

Part $($c$)$ Calculate the potential energy, Ebottom $,$ in

joules, stored in the stretched spring immediately

before you release it$.$

Part $($d$)$ Assume that the system has zero

gravitational potential energy at the lowest point of the

motion. Derive an expression for the total mechanical

energy, Eequilibrium, of the system as the monkey passes

through the equilibrium position in terms

of m$,$ x$,$ d$,$ g$,$ k$,$ and the speed of the monkey, ve$.$

Part $($e$)$ Calculate the speed of the monkey, ve$,$ in

meters per second, as it passes through equilibrium.

Part $($f$)$ Derive an expression for the total mechanical

energy of the system as the monkey reaches the top

of the motion, Etop, in terms of m$,$ x$,$ d$,$ k$,$ the maximum

height above the bottom of the motion, hmax $,$ and the

variables available in the palette.

Part $($g$)$ Calculate the maximum displacement, h$,$ in

centimeters, above the equilibrium position, that the

monkey reaches.

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