Can the potential energy in a simple harmonic motion be negative? Will it be so if we choose zero potential energy at some point other than the mean position?
No, the potential energy of the body in simple harmonic motion can never be negative because the minimum potential energy of the body can be zero at mean position. As the body crosses the mean position the potential energy keeps on increasing and it is maximum at extreme positions.
However, if we choose any other point other than mean position where potential energy is zero, then there is a possibility that the potential energy can be negative.