  In this paper, we consider the vibratory motions of lumped parameter systems
wherein the components of the system cannot be described by constitutive
expressions for the force in terms of appropriate kinematical quantities. Such
physical systems reduce to a system of differential-algebraic equations, which
invariably need to be solved numerically. To illustrate the issues with
clarity, we consider a simple system in which the dashpot is assumed to contain
a "Bingham" fluid for which one cannot describe the force in the dashpot as a
function of the velocity. On the other hand, one can express the velocity as a
function of the force.
