(a) Explanation Given information: Figure-(1) Figure-(1) represents the arrangement of the system. The mass of the slender rod is 3 kg , the mass of the disk is 5 kg , and the damping coefficient of the dashpot is 9 N ⋅ s / m . Write the expression for the moment of the forces about point A. ( m d r 2 2 + m r L 2 3 ) θ ¨ + m r g L 2 sin θ + c r 2 θ ˙ = 0 ..... (I) Here, the mass of the disk is m d , the mass of the rod is m r , radius of the disk is r , the length of the disk is L , the angular acceleration is θ ¨ , the angular velocity is θ ˙ , and the angular displacement is θ . Calculation: Substitute 5 kg for m d , 1 0 0 mm for r , 3 kg for m r , 9 N ⋅ s / m for c , 4 0 0 mm for L , θ for sin θ , and 9.81 m / s 2 for g in Equation (I). ( 5 kg × ( 1 0 0 mm ) 2 2 + 3 kg × ( 4 0 0 mm ) 2 3 ) θ ¨ + 3 kg × 9 (b) To determine The damping factor c c c .

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, Problem 19.164RP

(a)

To determine

The differential equations of the of the motion for small oscillations.

(b)

To determine

The damping factor ccc .

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Chapter 19, Problem 19.163RP

Chapter 19, Problem 19.165RP

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