Potential energy:

$\overline{){\mathbf{P}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

The energy required, E = ΔPE

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{\mathbf{(}}{{\mathbf{d}}}^{{\mathbf{2}}}{\mathbf{-}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{)}}}$

**a)**

E = (1/2)k(d^{2} - 0^{2}) = **(1/2)kd ^{2} **

During which interval is the largest amount of energy required to stretch the spring?

a) From x = 0 to x = d

b) From x = d to x = 2d

c) From x = 2d to x = 3d

d) The energy required is the same in all three intervals

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