Explanation Given information: The mass of the block ( m ) is 120 kg . The static deflection ( δ s t ) C is 15 mm or 0 .015m . The vertical periodic displacement ( δ ) is δ m sin ω f t . The forced circular frequency ( ω f ) is 18rad/s . The magnitude of displacement ( δ m ) is 10 mm of 0.010 m . The acceleration due to gravity ( g ) is 9 .81m/s 2 . Calculation: Show the deflection diagram of the beam ABC as Figure (1). Show the free body diagram of the block C as Figure (2). The expression deflection at the block C ( δ ′ ) as follows: δ ′ = − δ 2 Calculate the expression for the amplitude by considering the forces equilibrium using the relation: ∑ F = m a m x ¨ C = k ( δ ′ − x C ) Substitute − δ 2 for δ ′ . m x ¨ C = k ( − δ 2 − x C ) m x ¨ C = − k δ 2 − k x C m x ¨ C + k x C = − k δ 2 x ¨ C + k m x C = − k δ 2 Substitute δ m sin ω f t for δ . x ¨ C + k m x C = − k δ m sin ω f t 2 Calculate the natural circular frequency ( ω n 2 ) using the formula: ω n 2 = g ( δ s t ) C Substitute 9

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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 19.4, Problem 19.106P

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Find the maximum acceleration (aC)m of the block at C.

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Chapter 19.4, Problem 19.105P

Chapter 19.4, Problem 19.107P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the maximum acceleration ( a C ) m of the block at C .

Solution Summary: The author calculates the amplitude by considering the forces equilibrium using the relation: cdisplaystyle sum

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Find the maximum acceleration (aC)m of the block at C.

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Chapter 19 Solutions