(a) Explanation Given Information: The mass ( m ) of the block is 32 kg. The initial velocity ( v 0 ) of the block is 250 mm/s . The spring constant ( k ) is 12 kN/m . Calculation: Calculate the natural circular frequency ( ω n ) using the relation: ω n = k m Substitute 12 kN/m for k and 32 kg for m . ω n = ( 12 kN/m × 1000 N 1 kN ) 32 kg = 375 = 19.365 rad/s Calculate the period ( τ n ) using the relation: τ n = 2 π ω n Substitute 19 (b) To determine The amplitude ( x m ) of the motion and the maximum acceleration ( a m ) of the block.

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 19.1, Problem 19.4P

(a)

To determine

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

(b)

To determine

The amplitude (xm) of the motion and the maximum acceleration (am) of the block.

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Chapter 19.1, Problem 19.3P

Chapter 19.1, Problem 19.5P

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Chapter 19 Solutions

VECTOR MECHANIC

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

Solution Summary: The author calculates the period and frequency of the resulting motion using the relation comega.

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

The amplitude (xm) of the motion and the maximum acceleration (am) of the block.

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Chapter 19 Solutions