A spring of force constant \( k \) is first stretched by distance \( a \) from its natural lengt...

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A spring of force constant \( k \) is first stretched by distance \( a \) from its natural length and then further by distance \( b \). The work done in stretching the part \( b \) is
(a) \( \frac{1}{2} k a(a-b) \)
(b) \( \frac{1}{2} k a(a+b) \)
(c) \( \frac{1}{2} k b(a-b) \)
(d) \( \frac{1}{2} k b(2 a+b) \)
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