A non-ideal spring, when compressed or extended, exerts a force equal to:

F_{y} = -αy^{3}

where α is the spring constant.

Such non-ideal spring is placed vertically and compressed a distance L. A mass M is placed on the spring which is then released. Assume the spring is strong enough to push the mass in the air.

a) Find the work done by the spring to get back to the uncompressed position when it is released.

b) Find the speed of the mass M when the spring is back to its uncompressed length. (hint: the spring’s is not the only force)

c) Is the force of this non-ideal spring conservative? Explain.

Express you answer in terms of α ,L, M, and g. Check the units/dimensions for each answer.

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