The characteristic equation for a linear elastic system having zero na
tural frequencies to which a linear elasto-viscous oscillation damper
is attached is derived. It is shown that if this damper has one degree
of freedom and is not connected to a fixed base, the characteristic e
quation can be reduced to a form similar to that obtained for the case
when the elastic system has no zero natural frequencies. The problem
of finding the values of the damper parameters for which the minimum o
f all the attenuation decrements, corresponding to the least non-zero
natural frequencies, has the maximum possible value, is similar to the
same problem for a non-free elastic system.