  This paper investigates the behavior of a heavy soft spring in steady
circular motion. Since the spring is inhomogeneous due to centrifugal force,
one can rigorously prove that it follows the one-dimensional static Willis-form
equations. The theoretical predictions agree very well with experimental
results. It further demonstrates that these equations can give a clear
understanding of the stress-stiffening and spin-softening effect. These
findings reveal that the Willis-form equations can give very accurate linear
approximations of finite deformation problems and are also helpful to clarify
the classical concept of the principle of material frame indifference.
