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TYPES OF VIBRATION AND RELEVANT
UNDAMPED NATURAL VIBRATIONS
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acceleration analysis angular frequency Appendix applied force beam body Calculate co/con co2x constant cont cosh curve cycle cycle/s cyclic frequency damped natural oscillations damping coefficient damping factor dashpot deduce deflection degrees of freedom diagrammatically in Fig differential equation dynamic elastic electrical energy dissipated Engineering equation of motion equilibrium position estimate EXAMPLE excitation external forces forced vibration free-body diagram friction function fundamental frequency harmonic force Hence hysteretic instantaneous instrument kinetic energy length linear logarithmic decrement mass mathematical maximum value measured mechanical vibrations momentum N/mm natural frequency natural vibration non-dimensional periodic phase angle phase diagram phase plane pick-up plane angle quantity rad/s radian Referring to Fig relative represented resonant frequency Section shaft shown in Fig simple harmonic motion sinh solution sound pressure spring-mass system static static-equilibrium position strain energy time-line torque torsional oscillation undamped natural vertical vibrating system viscous damping wire zero