In an expression ½kx2 for the potential energy accumulates in the spring what does the x represent?        

Answer:

Quite frequently we consider there to be an object at one end of the spring while the other end of the spring is fixed in position example by being attached to a wall. x is the position of the thing measured with respect to its equilibrium position. The value of x symbolizes a position on an x-axis which is collinear with the spring and whose origin is at the equilibrium position. The symmetry position is the position of the entity for which the spring is neither stretched nor compressed.

The positive direction for the x-axis is classically chosen to be the direction in which one has to move the object from its equilibrium position in order to stretch the spring. In which case x is the amount by which the spring is stretched where a negative amount of stretch means the spring is actually compressed.

It is satisfactory to define the x-axis such that the positive direction is the direction in which one has to move the object from its equilibrium position in order to compress the spring. In which case x is the amount by which the spring is compressed where a negative amount of compression means the spring is actually stretched.