(a) Explanation Given information: The mass of the block ( m ) is 2 kg. The spring constant ( k ) is 128 N/m. The coefficient of viscous damping ( c ) is 0 .6 N ⋅ s / m . The upward velocity ( x ˙ ) is 0 .4m/s . Calculation: Calculate the critical damping coefficient ( c c ) using the formula: c c = 2 m ω n Substitute 2 kg for m and 8rad/s for ω n . c c = 2 × 2 × 8 = 32 N ⋅ s / m Calculate the log decrement using the formula: Log decrement = 2 π (b) To determine Find the maximum upward displacement ( x 3 ) of the block from equilibrium after two cycles.

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

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

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…

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Chapter 19.5, Problem 19.135P

(a)

To determine

Find the logarithm decrement.

(b)

To determine

Find the maximum upward displacement (x3) of the block from equilibrium after two cycles.

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Chapter 19.5, Problem 19.134P

Chapter 19.5, Problem 19.136P

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Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

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Find the logarithm decrement.

Solution Summary: The author calculates the logarithm decrement using the formula c.

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Find the logarithm decrement.

Find the maximum upward displacement (x3) of the block from equilibrium after two cycles.

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Chapter 19 Solutions