Explanation Given information: Figure-(1) represents the arrangement of the system. Figure-(1) The stiffness of the spring is k , the damping coefficient is c , the speed of the system is v , the amplitude is δ m , and the wavelength is L . Write the expression for the motion of the mass m . m x ¨ + k ( x − δ ) + c ( x ˙ − δ ˙ ) = 0 m x ¨ + c x ˙ + k x = k δ + c δ ˙ ..... (I) Here, the absolute velocity of the mass is ( x ˙ − δ ˙ ) , the displacement of the mass is x , and the displacement of the wheel is δ . Write the expression for the frequency of the wheel. ω f = 2 π v L ...... (II) Since, the wheel is moving according to sinusoidal wave, write the expression for the displacement of the wheel. δ = δ m sin ( ω f t ) ...... (III) Here, the time is t To determine (b) Derivation of the amplitude of the vertical displacement.

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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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 19.5, Problem 19.151P

To determine

(a)

The differential equations of the vertical displacement of the mass m.

To determine

(b)

Derivation of the amplitude of the vertical displacement.

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Chapter 19.5, Problem 19.150P

Chapter 19.5, Problem 19.152P

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Vector Mechanics for Engineers: Dynamics

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