(a) Explanation Given information: The impressed force ( P ) is P m sin ω f t . The equation of ( y ) is δ m sin ω f t . The natural frequency ( ω n ) is 120 Hz . The frequency of vibration ( ω f ) is 600 Hz . Calculation: The expression or the displacement transmitted ( x m ) as follows: x m = δ m 1 − ( ω f ω n ) 2 Calculate the forced response ( x ) using the relation: x = x m sin ω f t Substitute δ m 1 − ( ω f ω n ) 2 for x m . x = ( δ m 1 − ( ω f ω n ) 2 ) sin ω f t Calculate the relative motion ( z ) using the relation: z = x − y Substitute ( δ m 1 − ( ω f ω n ) 2 ) sin ω f t for x and δ m sin ω f t for y . z = ( δ m 1 − ( ω f ω n ) 2 ) sin ω f t − δ m sin ω f t z = [ δ m 1 − ( ω f ω n ) 2 − δ m ] sin ω f t z m = δ m 1 − ( ω f ω n ) 2 − δ m z m = δ m [ 1 1 − ( ω f ω n ) 2 − 1 ] Simplify the Equation (b) To determine Find the frequency ( f n ) at which the error is zero.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

Question

Chapter 19.4, Problem 19.122P

(a)

To determine

Find the percent error (E) when the frequency of the vibration is 600Hz.

(b)

To determine

Find the frequency (fn) at which the error is zero.

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Chapter 19.4, Problem 19.121P

Chapter 19.4, Problem 19.123P

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Chapter 19 Solutions

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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Find the percent error ( E ) when the frequency of the vibration is 600 Hz .

Solution Summary: The author calculates the percent error (E) when the frequency of the vibration is 600Hz.

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Find the percent error (E) when the frequency of the vibration is 600Hz.

Find the frequency (fn) at which the error is zero.

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Chapter 19 Solutions