Explanation Concept used: Write the expression for amplitude of forced vibration. x m = δ s t 1 − ( ω f 2 ω n 2 ) ...... (1) Here, x m is the amplitude of forced vibration, δ s r is the static displacement, ω f is the forced frequency and ω n is the natural frequency of system. Rearrange the above expression. x m δ s t = 1 1 − ( ω f 2 ω n 2 ) ...... (2) Write the expression for the magnitude of vibration caused by the periodic force. x m = ( P m / k ) 1 − ( ω f ω n ) 2 ...... (3) Here, P m is the amplitude of force. Write the expression for transmitted force amplitude. ( P t ) m = k x m Substitute ( P m / k ) 1 − ( ω f ω n ) 2 for x m in the above expression. ( P t ) m = k ( ( P m / k ) 1 − ( ω f ω n ) 2 ) Rearrange the above expression

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 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 19.121P

To determine

To show that ωfωn>2.

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Chapter 19.4, Problem 19.120P

Chapter 19.4, Problem 19.122P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....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 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A 10-Ib block A rests on a 40-Ib plate B that is...Ch. 19.1 - A 5-kg fragile glass vase is surrounded by packing...

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