A, because the mechanical energy of the object doing negative work is reduced by forces other than gravity and spring elasticity, the absolute value of the slope of the E-x image is equal to the magnitude of the tensile force on the object. As can be seen from the figure, the absolute value of the slope increases gradually in O ~ S 1, so the tension on the object increases gradually in O ~ S 1. So, A is wrong.

B, because the absolute value of the slope of the E-x image of the object in S 1 ~ S2 is unchanged, the tensile force on the object is unchanged. If the tension is equal to the gravity on the object, the object moves in a straight line at a uniform speed. Therefore, B is correct.

C, because the object in S 1 ~ S2 has the same tension and acceleration, it is impossible for the object to move in a straight line with variable acceleration, so C is wrong.

D. If the pulling force of the rope on the object is less than the gravity of the object in the range of 0 ~ S2, the object will move downward with acceleration, so the kinetic energy of the object will increase continuously, so D is correct.

So choose b and d.