(a) Explanation The position of a particle in spring at any instant is given by. y → = y 0 cos ω t (I) Here, y → is the position at a time t , y 0 is the initial position, ω is the angular frequency, and t is the time. Conclusion: The rate of change of position gives velocity. Hence differentiate equation (I) with respect to t. d y → d t = y 0 d ( cos ω t ) d t v → = − ω y 0 sin ω t (II) Rate of change of velocity is the acceleration. Thus, differentiate equation (II) with respect to t (b) To determine Is the acceleration is constant. (b) To determine Can the equations of motion is applicable for a particle in spring.

Physics for Scientists and Engineers: Foundations and Connections

15th Edition

ISBN: 9781305289963

Author: Debora M. Katz

Publisher: Cengage Custom Learning

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Chapter 2, Problem 68PQ

(a)

To determine

To show that ay→=−ω02y.

(b)

To determine

Is the acceleration is constant.

(b)

To determine

Can the equations of motion is applicable for a particle in spring.

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Chapter 2, Problem 67PQ

Chapter 2, Problem 69PQ

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Chapter 2 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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To show that a y → = − ω 0 2 y .

Solution Summary: The author explains how the rate of change of position gives velocity, hence differentiate equation (I) with respect to t.

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To show that ay→=−ω02y.

Is the acceleration is constant.

Can the equations of motion is applicable for a particle in spring.

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Chapter 2 Solutions