Explanation Given information: The mass of gear C is m, and the mass of gear A is 4m. Calculations: For the figures shown above: K i n e m a t i c s : 2 r θ A = r θ C 2 θ A = θ C 2 θ . A = θ . C L e t θ A = θ m 2 θ m = ( θ C ) m 2 θ . m = ( θ . C ) m F o r P o s i t i o n 1 : Kinetic energy: T 1 = 1 2 I ¯ A θ ˙ m 2 + 1 2 I ¯ C ( 2 θ ˙ m ) 2 + 1 2 I ¯ A B θ ˙ m 2 + 1 2 I ¯ C D ( 2 θ ˙ m ) 2 + 1 2 m A B ( l 2 θ ˙ m ) 2 + 1 2 m C D ( l 2 2 θ ˙ m ) 2 w h e r e , I ¯ A = 1 2 ( 4 m ) ( 2 r ) 2 = 8 m r 2 I ¯ C = 1 2 ( m ) ( r ) 2 = 1 2 m r 2 I ¯ A B = 1 12 m l 2 I ¯ C D = 1 12 m l 2 s u b s t i t u t i n g , T 1 = 1 2 m [ 8 r 2 + ( r 2 2 ) 4 + l 2 12 + l 2 3 + l 2 4 + l 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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Chapter 19.3, Problem 19.88P

To determine

The period of small oscillations of the system.

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Chapter 19.3, Problem 19.87P

Chapter 19.3, Problem 19.89P

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The period of small oscillations of the system.

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Chapter 19 Solutions