Question

the slinky acquires energy when it is compressed. why?

Answer 1

The slinky essentially wants to go back to its normal compressed position. You add work to the system when you apply a force to pull it. As a result there is potential energy in the spring, that will be converted to kintetic energy (the slinky moving back to its closed position).

The more the slinky is elongated, the more energy is added, up to a point. If you pull it too far, it will become deformed and the spring constant will be different. The x-value, elongation, will also be different because the neutral position has changed since the slinky is deformed. In other words, since it is deformed it will not naturally go back to the compressed position. Elongation and compression, x, is measured from the neural position.