(a) Explanation Given Information: The mass ( m ) of the block is 12 kg. The spring constant ( k ) is 5 kN/m . Calculation: The static elongation of the spring ( δ s t ) is equal to amplitude ( x m ) is 0.2222 in . . Calculate the natural circular frequency ( ω n ) using the relation: ω n = k m Substitute 5 kN/m for k and 12 kg for m . ω n = ( 5 kN/m × 1000 N 1 kN ) 12 = 416.667 = 20.412 rad/s Calculate the period ( τ n ) using the relation: τ n = 2 π ω n Substitute 20 (b) To determine The maximum velocity ( v m ) and maximum acceleration ( a m ) of the block.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Question

Chapter 19.1, Problem 19.5P

(a)

To determine

The period (τn) and frequency (fn) of the resulting motion.

(b)

To determine

The maximum velocity (vm) and maximum acceleration (am) of the block.

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Chapter 19.1, Problem 19.4P

Chapter 19.1, Problem 19.6P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P 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 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The period ( τ n ) and frequency ( f n ) of the resulting motion.

The period (τn) and frequency (fn) of the resulting motion.

The maximum velocity (vm) and maximum acceleration (am) of the block.

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Chapter 19 Solutions