When the charges are at the extreme positions, the velocities of both the charges will be zero.
DOUBT : Can we say that the net force acting on both the charges at the extreme position is also equal to zero?
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No, the net force acting on both the charges at the extreme points will not be zero. In fact, it will be maximum at the extreme points.
This is because, initially, when the system is released, there will be only electrostatic forces of repulsion between the two similar charges due to which they move apart from each other. However, as they move apart, the spring gets stretched due to which spring force acts on both the charges in the direction opposite to their motion (i.e. it tries to bring them closer). Note that since the charged objects have similar masses, the centre of mass of the system is exactly at the centre of the spring and assuming the system is released with no initial motion, it does not move as there is no external force acting on the system.
As the objects move apart by a certain distance (which you can calculate), the two forces (electrostatic and spring force) will cancel out each other. This is the mean position. Incidentally, at this point, the velocity of the two charges will be maximum after which the velocity starts decreasing as the spring force becomes stronger than the electrostatic force as the charges further move apart from the mean position. The velocity decreases till the charges stop and revert back. This is the extreme position and this is where the difference between the spring force and the electrostatic force is the maximum (and hence the net force on both the charges).
Hope this clears your doubts....