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 .
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 ...