(a) Explanation Given information: The mass ( m ) of the collar is is 4 kg. The amplitude ( P m ) of the force is 9 N. The circular frequency ( ω f ) is 5 rad/s . The amplitude ( x m ) of the collar is 150 mm. Calculation: Write the expression for natural circular frequency ( ω n ) : ω n 2 = k m Write the expression for amplitude of the motion ( x m ) : x m = P m k 1 − ω f 2 ω n 2 Substitute k m for ω n 2 . x m = P m k 1 − ω f 2 k m x m = (b) To determine The value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is out of phase with the applied force.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Chapter 19.4, Problem 19.100P

(a)

To determine

The value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is in phase with the applied force.

(b)

To determine

The value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is out of phase with the applied force.

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Chapter 19.4, Problem 19.99P

Chapter 19.4, Problem 19.101P

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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 - 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 value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is in phase with the applied force.

Solution Summary: The author calculates the value of the spring constant k, based on the mass and the circular frequency.

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The value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is in phase with the applied force.

The value of the spring constant k knowing that the motion of the collar has an amplitude of 150 mm and is out of phase with the applied force.

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Chapter 19 Solutions