Explanation Given information: The mass of the block A ( m A ) is 2.4 kg. The mass of the block B ( m B ) is 0.9 kg. The spring constant ( k ) is 180 N/m. The coefficient of damping ( c ) is 7 .5 N ⋅ s / m . The acceleration due to gravity ( g ) is 9 .81m/s 2 . Calculation: Calculate the natural circular frequency ( ω n ) using the formula: ω n = 2 k m A Here, k is the spring constant. Substitute 180 N/m for k and 2.4 kg for m A . ω n = 2 × 180 N/m 2.4 = 150 = 12.24745 rad/s Calculate the critical damping coefficient ( c c ) using the formula: c c = 2 m A ω n Substitute 2.4 kg for m A and 12 .24745rad/s for ω n . c c = 2 × 2.4 × 12.24745 = 58.7878 N ⋅ s / m Calculate the stretch at equilibrium using the relation: Stretch at equilibrium = m A g 2 k Substitute 2.4 kg for m A , 9 .81m/s 2 for g , and 180 N/m for k . Stretch at equilibrium = 2.4 × 9.81 2 × 180 = 0.0654 m Calculate the initial stretch using the relation: Initial Stretch = ( m A + m B ) g 2 k Substitute 2.4 kg for m A , 0.9 kg for m B , 9 .81m/s 2 for g , and 180 N/m for k . Initial Stretch = ( 2.4 + 0.9 ) × 9.81 2 × 180 = 0.089925 m Calculate the damping circular frequency ( ω d ) using the formula: ω d = ω n 1 − ( c c c ) 2 Substitute 12

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ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 19.5, Problem 19.137P

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Find the minimum tension (T) that will occur in each spring during the resulting motion.

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Chapter 19.5, Problem 19.136P

Chapter 19.5, Problem 19.138P

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Find the minimum tension ( T ) that will occur in each spring during the resulting motion.

Solution Summary: The author calculates the minimum tension ( T ) that will occur in each spring during the resulting motion.

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Find the minimum tension (T) that will occur in each spring during the resulting motion.

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Chapter 19 Solutions