In discussing the dynamic behavior of single degree-of-freedom systems, we assumed that in the model representing the structure, the restoring force was proportional to the displacement. We also assumed the dissipation of energy through a viscous damping mechanism in which the damping force was proportional to the velocity. In addition, the mass in the model was always considered to be unchanging with time. As a consequence of these assumptions, the equation of motion for such a system resulted in a linear, second-order ordinary differential equation with constant coefficients, namely,
$$ m\ddot y + c\dot y + ky = F\left( t \right) $$
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© Springer Science+Business Media Dordrecht 1991