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Ralph E. Blake - Cooper Union

CHAPTER 2 BASIC VIBRATION THEORYR alph E. BlakeINTRODUCTIONThis chapter presents the theory of free and forced steady-state vibration of singledegree-of-freedom systems. Undamped systems and systems having viscous damp-ing and structural damping are included. Multiple degree-of-freedom systems arediscussed, including the normal-mode theory of linear elastic structures andLagrange s PARTS OF VIBRATORY SYSTEMSV ibratory systems comprise means for storing potential energy (spring), means forstoring kinetic energy (mass or inertia), and means by which the energy is graduallylost (damper). The vibration of a system involves the alternating transfer of energybetween its potential and kinetic forms. In a damped system, some energy is dissi-pated at each cycle of vibration and must be replaced from an external source if asteady vibration is to be maintained.

n at time t = 0.Thus,the conditions of displacement and velocity which exist at zero time determine the subsequent oscillation completely. Phase Angle.Equation (2.5) for the displacement in oscillatory motion can be written, introducing the frequency relation of Eq. (2.6), x = A sin ω nt + B cos ω nt = C sin (ω nt +θ) (2.9)

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