Explanation Given information: The weight of the imbalanced rotating mass is 1 lb , the radius of rotating mass is 6 in , the rotational speed tail is 500 rpm , the total weight of the system is 165 lb , the equivalent stiffness is 8800 lb / ft and the damping ratio is 0.15 . Write the expression of mass of imbalanced weight. m = w g ..... (I) Here, the imbalanced ass is m , the acceleration due to gravity is g and the imbalanced weight is w . Write the expression of mass of the system. M = W g ...... (II) Here, the mass of the system is M , the total weight of the system is W . Write the expression of the frequency of periodic force. ω f = 2 π N 60 ...... (III) Here, the rotational speed is N , the frequency of periodic force is ω f . Write the expression for the amplitude of applied force. P m = m r ω f 2 ...... (IV) Here, the radius of rotating mass is r , the amplitude of applied force is P m . Write the expression of damping coefficient. c = 2 ζ k M ....... (V) Here, the damping coefficient is c , the equivalent stiffness is k and the damping ratio is ζ . Write the expression of amplitude of steady state response of the system. X m = P m [ k − ( M ω f 2 ) 2 ] 2 + ( c ω f ) 2 ...... (VI) Here, the amplitude is X m . Calculation: Substituting 1 lb for w , 32.185 ft / s 2 for g in Equation (I): m = 1 lb 32.185 ft / s 2 = 0.0310 lb ⋅ s 2 / ft Substituting 165 lb for W and 32.185 ft / s 2 for g in Equation (II): M = 165 lb 32.185 ft / s 2 = 5.1266 lb ⋅ s 2 / ft Substituting 500 rpm for N in Equation (III): ω f = 2 π ( 500 rpm ) 60 = 0.1047 ( 500 rpm ) = 52.35 rad / s Substituting 0.0310 lb ⋅ s 2 / ft for m , 6 in for r , and 52.35 rad / s for ω f in Equation (IV): P m = ( 0.0310 lb ⋅ s 2 / ft ) ( 6 in ) ( 52

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Author: BEER

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 19.5, Problem 19.145P

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The amplitude of vibration of the tail section.

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Chapter 19.5, Problem 19.144P

Chapter 19.5, Problem 19.146P

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The amplitude of vibration of the tail section.

Solution Summary: The author explains the amplitude of vibration of the tail section, the rotational speed tail, and the damping ratio.

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The amplitude of vibration of the tail section.

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