Explanation Given information: A uniform rod AB can rotate in a vertical plane about a horizontal axis at C located at a distance c above the mass center G of the rod. Calculations: From the figure shown above: k i n e t i c e n e r g y a t p o s i t i o n 1 : T 1 = 0 P o t e n t i o l e n e r g y a t p o s i t i o n 1 : V 1 = m g h w h e r e , h = c ( 1 − cos θ m ) V 1 = m g c ( 1 − cos θ m ) [ 1 − cos θ m = 2 sin 2 θ m 2 f o r s m a l l v a l u e o f θ m ; 1 − cos θ m ≈ 2 ( θ m 2 ) 2 = θ m 2 2 ] ∴ V 1 = m g c θ 2 m 2 A t P o s i t i o n 2 : k i n e t i c e n e r g y a t P o s i t i o n 2 : T 2 = 1 2 I C θ . m 2 w h e r e , I C → M o m e n t o f i n e r t i a o f t h e r o d a b o u t p o int C ( I C = I ¯ + m c 2 = 1 12 m l 2 + m c 2 ) ∴ T 2 = 1 2 m ( l 2 12 + c 2 ) θ

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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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 19.3, Problem 19.75P

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The value of C for which the frequency of the motion will be maximum.

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Chapter 19.3, Problem 19.74P

Chapter 19.3, Problem 19.76P

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The value of C for which the frequency of the motion will be maximum.

Solution Summary: The author calculates the value of C for which the frequency of the motion will be maximum.

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The value of C for which the frequency of the motion will be maximum.

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