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W = K(final) - K(initial) + U(final) - U(initial) . . . . (1)

as we define Potential energy as negative of work done by conservative force and assuming that the only force in this situation is Spring force then ,

W(spring) = K(final) - K(initial)

As work done is calculated by finding component of spring force in direction of displacement. How can we say that U(final) - U(initial) applies for all possible conditions of extension of spring as displacement may not be in direction of force ?

Spring force = 0.5kx

^{2}