  We consider model order reduction of a nonlinear cable-mass system modeled by
a 1D wave equation with interior damping and dynamic boundary conditions. The
system is driven by a time dependent forcing input to a linear mass-spring
system at one boundary. The goal of the model reduction is to produce a low
order model that produces an accurate approximation to the displacement and
velocity of the mass in the nonlinear mass-spring system at the opposite
boundary. We first prove that the linearized and nonlinear unforced systems are
well-posed and exponentially stable under certain conditions on the damping
parameters, and then consider a balanced truncation method to generate the
reduced order model (ROM) of the nonlinear input-output system. Little is known
about model reduction of nonlinear input-output systems, and so we present
detailed numerical experiments concerning the performance of the nonlinear ROM.
We find that the ROM is accurate for many different combinations of model
parameters.
