(a) Explanation Given information: The weight of the block A ( W ) is 18 lb . The spring constant ( k ) is 8 lb/ft . The magnitude of the acceleration ( a ) is a m sin ω f t . The maximum acceleration ( a m ) is 5 ft/s 2 . The forced circular frequency ( ω f ) is 6rad/s . The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Calculate the maximum acceleration of the forced vibration ( a m ) using the formula: a m = − δ m ω f 2 Here, δ m is the deflection of the spring due to the periodic force. Substitute 5 ft / s 2 for a m and 6 rad / s for ω f . 5 ft / s 2 = − δ m ( 6 rad / s ) 2 δ m = − 5 36 δ m = − 0.13889 ft Calculate the mass of the block A ( m ) using the formula: W = m g m = W g Substitute 18 lb for W and 32.2 ft / s 2 for g . m = 18 lb 32.2 ft / s 2 = 0.559 lb ⋅ s 2 / ft Calculate the natural circular frequency of oscillation ( ω n ) using the formula: ω n = k m Substitute 8 lb / ft for k and 0 (b) To determine Find the amplitude of the fluctuating force ( F m ) exerted by the spring on the block.

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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Chapter 19.4, Problem 19.111P

(a)

To determine

Find the maximum displacement (xm) of block A.

(b)

To determine

Find the amplitude of the fluctuating force (Fm) exerted by the spring on the block.

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Chapter 19.4, Problem 19.110P

Chapter 19.4, Problem 19.112P

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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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Find the maximum displacement ( x m ) of block A .

Solution Summary: The author calculates the maximum displacement of block A using the formula: (x_m).

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Find the maximum displacement (xm) of block A.

Find the amplitude of the fluctuating force (Fm) exerted by the spring on the block.

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Chapter 19 Solutions