An Ideal Spring w/ a Spring Constant Problem. Please help me!?

Question

An ideal spring with a spring constant of 18 N/m is suspended vertically. A body of mass 0.60 kg is attached to the unstretched spring and released.

(a) What is the extension of the spring when the speed is a maximum?
_______meters

(b) What is the maximum speed?
_______m/s

Answer 1

I like to use energy to solve these spring problems since
m*g*y=.5*k*y^2+.5*m*v^2
or
2*m*g*y-k*y^2=m*v^2
v=sqrt(2*g*y-k*y^2/m)

take the first derivative of dv/dy using the chain rule
dv/dy=2*(2*g-2*k*y/m)/
sqrt(2*g*y-k*y^2/m))

set equal to zero and solve for y
g*m/k=y

plugging in the numbers and using g=9.8
y=0.33 m
and
v=1.79 m/s

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