TABLE OF CONTENTS The mechanical impedance at a given point in a vibratory system is the ratio of the sinusoidal force applied to the system at that point to the velocity at the same point. For example, mechanical impedance is discussed in Chap. 6 as it relates to dynamic absorbers and auxiliary mass dampers. In the following sections of this chapter, the mechanical impedance of basic elements that make up vibratory systems is presented. This is followed by a discussion of combinations of these elements. Then, various mechanical circuit theorems are described. Such theorems can be used as an aid in the modeling of mechanical circuits and in determining the response of vibratory systems; they are the mechanical equivalents of well-known theorems employed in the analysis of electric circuits. The measurement of mechanical impedance and some applications are also given.
The mechanical impedance Z of a system is the ratio of a sinusoidal driving force F acting on the system to the resulting velocity v of the system. Its mechanical mobility 
is the reciprocal of the mechanical impedance.
Consider a sinusoidal driving F that has a magnitude F 0 and an angular frequency ?:
The application of this force to a linear mechanical system results in a velocity v:
where v 0 is the magnitude of the velocity and ? is the phase angle between F and v.
Then by definition,...
