Explanation Given information: The weight ( W d i s k ) of the disk is 12 lb. The weight ( W A B ) of the rod AB is 20 lb. The spring constant ( k ) is 30 lb/in . Assume the acceleration due to gravity ( g ) as 32.2 ft/s 2 . Calculation: Show the position 1 and position 2 of the system with velocity as in Figure (1). For position 1: Calculate the mass of the disk ( m d i s k ) using the relation: m d i s k = W d i s k g Substitute 12 lb for W d i s k and 32.2 ft/s 2 for g . m d i s k = 12 32.2 = 0.373 lb ⋅ s 2 / ft Calculate the mass of the rod AB ( m A B ) using the relation: m A B = W A B g Substitute 20 lb for W A B and 32.2 ft/s 2 for g . m A B = 20 32.2 = 0.621 lb ⋅ s 2 / ft Write the expression for the kinetic energy ( T 1 ) : T 1 = 0 Write the expression for the potential energy ( V 1 ) : V 1 = 1 2 k x m 2 Here, x m is maximum spring deformation. For position 2: Write the expression for the kinetic energy ( T 2 ) : T 2 = 1 2 m A B v m 2 + ( 1 2 m d i s k r 2 ) ( v m r ) 2 + m d i s k v m 2 = 1 2 ( m A B + 3 m d i s k ) v m 2 Write the expression for the potential energy ( V 2 ) : V 2 = 0 For simple harmonic function the maximum velocity ( v m ) : v m = ω n x m Write the expression for the conservation of energy: T 1 + V 1 = T 2 + V 2 Substitute 0 for T 1 , 1 2 k x m 2 for V 1 , 1 2 ( m A B + 3 m d i s k ) v m 2 for T 2 , and 0 for V 2

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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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.3, Problem 19.90P

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The frequency (fn) of vibration of the system.

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Chapter 19.3, Problem 19.89P

Chapter 19.3, Problem 19.91P

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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 vibration of the system.

Solution Summary: The author shows the position 1 and position 2 of the system with velocity as in Figure (1).

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The frequency (fn) of vibration of the system.

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Chapter 19 Solutions