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But what I thought was; they are saying NET work done ON the sample .. doesn't that mean work done by stretching a spring (or work done by us). Had they asked Net Work Done BY THE SAMPLE, Z should have been the answer?When you stretch a spring, we do work. If we then release the spring, some of the energy is recovered. Some is lost. When they say " net " work done, they're talking about the total work done.
The arrows going up signify that the spring is being loaded, and thus we call it the loading phase. The arrow that's going down is when the spring is released, it's now compressing. This is called the unloading phase. The area which is X and Y, is commonly known as " Hysteresis ".
Hysteresis is basically the energy lost during the stretching and releasing. This leaves us with Z, which is said to be the net work done.
My advice to you would be to think that whatever is outside that area of hysteresis, is the net work done. Hope that helps ^_^