ABSTRACT
In order to aid understanding, a single degree of freedom (SDOF) system consists of a spring of stiffness (k), a mass (m), and a damper, again considered here and shown in Figure 5.1. The equilibrium dynamic equation at time t is written as
Fi(t) + Fc(t) + Fs(t) = F(t) (5.1)
⇒ Inertia force + Damping force + Stiffness force = External force
⇒ m a(t) + c v(t) + k y(t) = F(t) (5.2)
where a(t), v(t), and y(t) are, respectively, the acceleration, velocity, and displacement of the SDOF system at time t. In general, any vibrating object consists of three types of vibration responses: acceleration, velocity, and displacement responses. All these parameters are interrelated, which implies that the measurement of one parameter may be used to generate any of the other parameters through integration or differentiation.
