  We consider two different forms for a relativistic version of a linear
restoring force. The pair comes from taking Hooke's law to be the force
appearing on the right of the relativistic expressions: dp/dt or dp/dtau .
Either formulation recovers Hooke's law in the non-relativistic limit. In
addition to these two forces, we introduce a form of retardation appropriate
for the description of a linear (in displacement) force arising from the
interaction of a pair of particles with a relativistic field. The procedure is
akin to replacing Coulomb's law in E&M with a retarded form (the first
correction in the full relativistic case). This retardation leads to the
expected oscillation, but with amplitude growth in both its relativistic and
non-relativistic incarnations.
