Where is the fault in the mechanical energy conservation in a spring block system here?

Question

Consider a spring block system . The surface on which the block moves is frictionless and the air resistance is nil . Suppose the block is at the mean position in it's natural length . By hookes law , ( PE ) = 0 because x = 0 . Also , the ( KE ) = 0 because block is at rest . Hence , total mechanical energy = KE + PE = 0 . Now , suppose it is elongated to maximum elongation . Then , at the point of maximum elongation ; KE = 0 and PE = k.a² / 2 , where a is the maximum displacement of elongtion . Hence , at this point , Mechanical energy = KE + PE = 0 + k.a²/2 = k.a²/2 . It is evident that initial mechanical energy ( = 0 ) is not equal to final mechanical energy ( ka²/2 ) . But how ?

Answer 1

Energy is added to the system by the force that pulled the mass to position $a$.

Using conservation of energy to make predictions about a system requires the concepts of “closed” and “open” systems.