What factors affect the displacement range in Hooke's Law?

[Grhymn]

I was told that Hooke's Law (F=-kx) only accounts for small displacements. But for some objects the displacement can be greater than with others. I was wonderinig which quality of the objects is responsible for this?

 

[Mapes]

I was told that Hooke's Law (F=-kx) only accobunts for small displacements. But for some objects the displacement can be greater than with others. I was wonderinig which quality of the objects is responsible for this?

Actually, Hooke's Law is limited to small strains (displacement normalized to initial length). So a long elastic object, when stretched, could produce a larger displacement in the linear regime compared to a shorter object.

The limited linear regime arises for most materials because atoms can only be stretched so far before it becomes energetically favorable for them to break instead. Even the linear model is only an approximation to a more complicated relationship between bonded atoms.*

*(If you're really interested: Any equilibrium energy well can be approximated as a parabola for small displacements, and the quadratic form of strain energy gives rise to a linear restoring force that increases with displacement and is equivalent to Hooke's Law.)