Explanation Given information: A uniform rod of length L is supported by a ball and socket joint at A and by a vertical wire CD. Calculations: The figure shown above represents the maximum displacement . F r o m t h e f i g u r e a t r i g h t , t h e h o r i z o n t a l d i s p l a c e m e n t o f C : x C = b θ m From the left figure: ϕ m = x C h = b h θ m y C = h ( 1 − cos ϕ m ) ≈ 1 2 h ϕ m 2 y C = 1 2 h ( b h θ m ) 2 = 1 2 b 2 h θ m 2 ∴ y ¯ m = y G = A G A C − y C = 1 2 L b ( 1 2 b 2 h θ m 2 ) y ¯ m = 1 4 ⋅ b L h θ m 2 Hence, the kinetic and potential energies for the above position will be: T 1 = 0 V 1 = m g y m = 1 4 m g b L h θ m 2 The figure shown above represents position 2 with maximum velocity . The kinetic and potential energies will be: T 2 = 1 2 I ¯ θ ˙ m 2 + 1 2 m v ¯ m 2 = 1 2 ( 1 12 m L 2 ) θ ˙ m 2 + 1 2 m ( L 2 C ) 2 T 2 = 1 6 m L 2 θ ˙ m 2

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

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

Publisher: McGraw-Hill Education

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 19.3, Problem 19.94P

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The expression for the period of oscillation.

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Chapter 19.3, Problem 19.93P

Chapter 19.3, Problem 19.95P

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The expression for the period of oscillation.

Solution Summary: The author explains the expression for the period of oscillation of the rod.

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The expression for the period of oscillation.

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Chapter 19 Solutions