How do we know if a string s extending elastically?

It will return to its original length or shape when the force is removed.

Hi Jamaal

You can plot a graph of extension against load as you increase the force (or load) on the material, and then plot the points as you unload it. If it has not been taken beyond the elastic limit, then you should find that the points plotted as you are unloading follow the same line. (Don't forget to allow the system to settle before taking each reading). In other words it has returned to its original shape and size when the deforming load has been removed.