2Vibration of Discrete Systems: Brief Review
2.1 VIBRATION OF A SINGLE‐DEGREE‐OF‐FREEDOM SYSTEM
The number of degrees of freedom of a vibrating system is defined by the minimum number of displacement components required to describe the configuration of the system during vibration. Each system shown in Fig. 2.1 denotes a single‐degree‐of‐freedom system. The essential features of a vibrating system include: (i) a mass m, producing an inertia force: 
; (ii) a spring of stiffness k, producing a resisting force: kx; and (iii) a damping mechanism that dissipates the energy. If the equivalent viscous damping coefficient is denoted as c, the damping force produced is 
.
Figure 2.1 Single‐degree‐of‐freedom systems.
2.1.1 Free Vibration
In the absence of damping, the equation of motion of a single‐degree‐of‐freedom system is given by
where 
is the force acting on the mass and 
is the ...
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