A child's toy consists of a m = 36 g monkey suspended from a spring of negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 11.7 cm. This toy is so adorable you pull the monkey down an additional d = 5.7 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down.

Part (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring.

Part (b) Draw the free-body diagram that best represents the forces acting on the monkey as you are pulling ti down, immediately before you let go.

Part (c) Calculate the potential energy, E
b
o
t
t
o
m
, 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, E
e
q
u
i
l
i
b
r
i
u
m
, 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, v
e
.