(a) Explanation Given information: The unbalance weight ( w ) is 14 oz. The radius of the circle ( r ) is 6 inch. The weight of the system ( W ) is 300 lb. The speed of the exciter ( N ) is 1200 rpm. The amplitude of vibration ( x m ) is 0.6 inch. The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Convert the unit of unbalance weight ( w ) from oz to lb: w = ( w ) oz × 1 lb 16 oz Here, ( w ) oz is the unbalance weight. Substitute 14 oz for ( w ) oz . w = 14 oz × 1 lb 16 oz = 0 .875 lb Calculate the mass of the unbalance weight ( m ) using the formula: m = w g Substitute 0.875 lb for w and 32.2 ft / s 2 for g . m = 0.875 lb 32.2 ft / s 2 = 0.02717 lb ⋅ s 2 / ft Calculate the mass of the system ( M ) using the formula: M = W g Substitute 300 lb for W and 32.2 ft / s 2 for g . M = 300 lb 32.2 ft / s 2 = 9.3167 lb ⋅ s 2 / ft Calculate the frequency of the periodic force ( ω f ) using the relation: ω f = 2 π N 60 Substitute 1200 rpm for N . ω f = 2 π ( 1 , 200 rpm ) 60 = 125 (b) To determine The damping factor ( c c c ) .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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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…

Question

Chapter 19.5, Problem 19.143P

(a)

To determine

The combined spring constant (k).

(b)

To determine

The damping factor (ccc).

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Chapter 19.5, Problem 19.142P

Chapter 19.5, Problem 19.144P

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Chapter 19 Solutions

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 combined spring constant ( k ).

Solution Summary: The author calculates the mass of the unbalance weight using the formula: m=wg.

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The combined spring constant (k).

The damping factor (ccc).

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Chapter 19 Solutions