Explanation Given information: Deflection of the beam δ A = P l 3 48 E I Length L = 15 f t Modulus of elasticity E = 30 × 10 6 p s i And, Moment of inertia I = 2 × 10 − 3 f t 4 From figure: k = P δ s t k = P P L 3 / 48 E I < To determine (b) The frequency of vibration of the block attached to the center of the beam.

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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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 19.1, Problem 19.27P

To determine

(a)

The equivalent spring constant of the beam.

To determine

(b)

The frequency of vibration of the block attached to the center of the beam.

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Chapter 19.1, Problem 19.26P

Chapter 19.1, Problem 19.28P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Dynamics

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(a) The equivalent spring constant of the beam.

Solution Summary: The author explains the equivalent spring constant of the beam, which is k=853.33psi.