What's wrong with this Spring Energy question?

[cadenmoore]

Homework Statement

You are given a spring with some peculiar properties. Rather than
the usual equation F = −kx, you find the spring is best modeled
by the equation F = −kx − lambda(|x|^2)(xhat), where lambda has units of N/m^2.
The unstretched length of the spring is x0. You attach the spring
to the ceiling and hang an object of mass M from the spring.
(a) Calculate the expression for the potential energy
stored in the spring.
(b) Using the energy principle, determine how much the
spring stretches when the mass is hung from it.
Express your answer in terms of the quantities given
in the problem. (Hint: define the zero of gravitational
potential at the equilibrium length of the spring.)
Now you mount the spring horizontally against a wall next to a
frictionless surface and place the mass against the spring. Then
you push on the mass until the spring is compressed to 1/4 its
equilibrium length.
(c) After releasing the mass, what is its final velocity?

Homework Equations

Us=1/2kx^2
Fs=-kx
Ef=Ei (+W)
KE=1/2mv^2

The Attempt at a Solution

This actually isn't a problem I'm trying to solve. I'm trying to figure out what's wrong with it. My professor said there's a fundamental error in the composition of the problem in part (b). Does anyone see what's wrong with it?

 

[Andrew Mason]

If you apply energy considerations to Part b (spring energy = change in gravitational potential energy) you do not get the extension of the spring with the stationary mass hanging from it. You would get its maximum amplitude of oscillation.

AM