Explanation Given information: The mass of the two uniform rod is m . The length of the two uniform rod is l . The spring constant is k . Calculation: Show the free body diagram equation as in Figure (1). Calculate the distance ( d ) by apply Pythagoras theorem: d 2 = l 2 + ( l 2 ) 2 = l 2 + l 2 4 = 5 l 2 4 Take moment about C in the system for external forces. ( ∑ M C ) e x t e r n a l = − m g l 2 sin θ − m g l 2 θ − k l 2 θ For small oscillation sin θ ≈ θ . ( ∑ M C ) e x t e r n a l = − m g l 2 θ − m g l 2 θ − k l 2 θ = − m g θ − k l 2 θ Take moment about C in the system for effective forces. ( ∑ M C ) e f f e c t i v e = 2 m l 2 θ ¨ 12 + ( m l θ ¨ 4 × l ) + ( m d θ ¨ ) d = 2 m l 2 θ ¨ 12 + ( m l 2 θ ¨ 4 ) + ( m d 2 θ ¨ ) Substitute 5 l 2 4 for d 2 . ( ∑ M C ) e f f e c t i v e = 2 m l 2 θ ¨ 12 + ( m l 2 θ ¨ 4 ) + ( m × 5 l 2 4 θ ¨ ) = 2 m l 2 θ ¨ 12 + ( m l 2 θ ¨ 4 ) + ( 5 m l 2 4 θ ¨ ) Equate the moment about C in the system for external and effective forces

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

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

Publisher: McGraw-Hill Education

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Gen…

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Chapter 19.2, Problem 19.56P

To determine

The frequency (fn) of small oscillation of the system.

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Chapter 19 Solutions

Connect 1 Semester Access Card for 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 frequency ( f n ) of small oscillation of the system.

Solution Summary: The author shows the free body diagram equation as in Figure (1). The distance is calculated by applying Pythagoras theorem.

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The frequency (fn) of small oscillation of the system.

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Chapter 19 Solutions