(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.

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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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 19.5, 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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Chapter 19 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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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