Explanation Given information: The weight of the block ( W ) is 64 lb . The spring constant ( k ) is 1 kip/ft . The magnitude of the force ( P ) is P m sin ω f t . The forced circular frequency ( ω f ) is 10 rad/s . The amplitude of motion ( x m ) is 0.75 in . or 0.0625 ft . The acceleration due to gravity ( g ) is 32.2 ft/s 2 . Calculation: Calculate the mass of the block ( m ) using the formula: W = m g m = W g Substitute 64 lb for W and 32.2 ft/s 2 for g . m = 64 32.2 = 1.9876 lb ⋅ s 2 / ft Calculate the natural circular frequency ( ω n ) using the formula: ω n = k m Substitute 1 kip/ft for k and 1.9876 lb ⋅ s 2 / ft for m . ω n = 1 × 1000 lb/ft 1.9876 lb ⋅ s 2 / ft = 22

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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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.4, Problem 19.102P

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Find the constant force (Pm).

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Chapter 19.4, Problem 19.101P

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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 constant force ( P m ) .

Solution Summary: The author calculates the mass of the block (m) using the formula: cW=mg m=

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