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A block is attached to a spring obeying Hooke's law ($F = -kx$). The block is held a distance $d$ from the equilibrium position.

The change in the potential energy of the spring when the block is moved to a distance $2d$ from its equilibrium position is

A

$ \cfrac {3}{2}{kd}^2 $

B

$ {kd}^2 $

C

$ \cfrac {1}{2} {kd}^2 $

D

$ \cfrac {1}{4}{kd}^2 $

E

$ {3kd}^2 $

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