a. Explanation Given data: The velocity versus time graph is shown in Figure P14.58. Amplitude is doubled and frequency is halved. Formula used: Write the expression for maximum velocity. v max = 2 π f A (1) Here, f is the frequency, and A is the amplitude. Explanation: Refer to Figure P14.58, write the expression for velocity. v x ( t ) = v max cos ( 2 π f t ) (2) Here, v max is the maximum velocity, f is the frequency, and t is the time interval. Modify equation (1) for first new values as follows. v max ( new1 ) = 2 π f new1 A new1 Substitute 2 A for A new1 and 1 2 f for f new1 , v max ( new1 ) = 2 π ( 1 2 f ) ( 2 A ) = 2 π f A Substitute v max for 2 π f A , v max ( new1 ) = v max Substitute 2 m s for v max , v max ( new1 ) = 2 m s Find the value of f . f = 1 T Substitute 4 s for T , f = 1 4 s = 0.25 Hz Modify equation (2) for first new values as follows. v x ( new1 ) ( t ) = v max ( new1 ) cos ( 2 π f new1 t ) Substitute 2 m s for v max ( new1 ) and 1 2 f for f new1 , v x ( new1 ) ( t ) = ( 2 m s ) cos ( 2 π ( 1 2 f ) t ) = ( 2 m s ) cos ( π f t ) Substitute 0.25 Hz for f , v x ( new1 ) ( t ) = ( 2 m s ) cos ( ( 0.25 Hz ) π t ) (3) Substitute 1 s for t , v x ( new1 ) ( 1 s ) = ( 2 m s ) cos ( ( 0.25 Hz ) π ( 1 s ) ) = 2 m s Substitute 2 s for t in equation (3), v x ( new1 ) ( 2 s ) = ( 2 m s ) cos ( ( 0.25 Hz ) π ( 2 s ) ) = 0 m s Substitute 3 s for t in equation (3), v x ( new1 ) ( 3 s ) = ( 2 m s ) cos ( ( 0 b. To determine To draw: The velocity graph when the amplitude and spring constant are same and the mass is quadrupled.

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

4th Edition

ISBN: 9780134700502

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 14, Problem 58GP

To determine

To draw: The velocity graph when the amplitude is doubled and the frequency is halved.

To determine

To draw: The velocity graph when the amplitude and spring constant are same and the mass is quadrupled.

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Chapter 14, Problem 57GP

Chapter 14, Problem 59GP

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Chapter 14 Solutions

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

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