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sign of potential energy of SHO

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Suppose the particle is at distance x from mean position and moving away . The standard formula for calculating potential U is U=-w here wis the work w=kxdx when the particle is moving away .On integration U=1/2Kx^2 . When the particle is moving towards mean position w=-kxdx on integration U=-1/2kx^2 thus the sign changes with direction Is it correct

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