Explanation Calculation: Show the free body diagram of the system of two blocks with force acting as in Figure (1). Consider for load A . The expression for the forces acting in vertical direction in the block A as follows; P m sin ω f t + 2 k ( x B − x A ) + c ( x ˙ B − x ˙ A ) = m x ¨ A m x ¨ A − 2 k ( x B − x A ) − c ( x ˙ B − x ˙ A ) = P m sin ω f t m x ¨ A − [ − 2 k ( x A − x B ) ] − [ − c ( x ˙ B − x ˙ A ) ] = P m sin ω f t m x ¨ A + 2 k ( x A − x B ) + c ( x ˙ B − x ˙ A ) = P m sin ω f t Consider for load B . The expression for the forces acting in vertical direction in the block B as follows; − 2 k ( x B − x A ) − c ( x ˙ B − x ˙ A ) − k x B − 2 c x ˙ B = m x ¨ B − [ − 2 k ( x A − x B ) ] − [ − c ( x ˙ A − x ˙ B

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…

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Chapter 19.5, Problem 19.152P

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Write the differential equation defining the displacement xA and xB of the two blocks from their equilibrium position.

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Chapter 19.5, Problem 19.151P

Chapter 19.5, Problem 19.153P

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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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Write the differential equation defining the displacement x A and x B of the two blocks from their equilibrium position.

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Write the differential equation defining the displacement xA and xB of the two blocks from their equilibrium position.

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Chapter 19 Solutions