Explanation Given information: The weight of the machine ( W ) is 800 lb. The spring constant ( k ) is 200 lb/inch. The coefficient of damping ( c ) is 8 lb ⋅ s / in . . The periodic force is applied with a frequency ( f f ) is 2.5 cycles. The magnitude of the periodic force ( P m ) is 30 lb. Calculation: Convert the damping coefficient ( c ) from lb ⋅ s / in . to lb ⋅ s / ft : c = ( c ) lb ⋅ s / in . × lb ⋅ s 1 in . × 1 ft 12 in . Here, ( c ) lb ⋅ s / in . is the damping coefficient in lb ⋅ s / in . . Substitute 8 lb ⋅ s / in . for c . c = 8 × lb ⋅ s 1 in . × 1 ft 12 in . = 96 lb ⋅ s / ft Calculate the mass of the machine ( m ) element using the formula: m = W g Here, g is the acceleration due to gravity. Substitute 800 lb for W and 32.2 ft / s 2 for g . m = 800 lb 32.2 ft / s 2 = 24.845 lb ⋅ s 2 / ft The system consists of two springs each with a spring constant of 200 lb / in . Thus, the spring constant of the system is given by two times the spring constant of 200 lb / in . . Calculate the spring constant of the system ( k ) for two springs using the relation: k = 2 k s p r i n g Here, k is the spring constant of the system and k s p r i n g is the spring constant of each spring. Substitute 200 lb / in . for k s p r i n g . k = 2 ( 200 lb / in . ) = 400 lb / in . = 400 lb 1 in . × 1 ft 12 in . = 4800 lb / ft Calculate the natural circular frequency ( ω n ) using the formula: ω n = k m Substitute 4800 lb / ft for k and 24.845 lb ⋅ s 2 / ft for m . ω n = 4800 lb / ft 24.845 lb ⋅ s 2 / ft = 13

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Forced undamped vibrations

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Chapter 19.5, Problem 19.139P

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The amplitude (xm) of the steady state vibration of the element.

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Chapter 19.5, Problem 19.138P

Chapter 19.5, Problem 19.140P

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Chapter 19 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The amplitude ( x m ) of the steady state vibration of the element.

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The amplitude (xm) of the steady state vibration of the element.

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