(a) Explanation Given information: The weight ( W ) of the flywheel is 500 lb. The spring constant ( k ) is 85 lb/in . The period ( τ ) of vibration of the flywheel is 0.5 sec. The radius ( r ) of the flywheel is 18 in . . The linear displacement ( x ) is 1.5 in . . The acceleration due to gravity is ( g ) is 32 .2 ft / s 2 . Calculation: Show the free-body-diagram equation as in Figure (1). Write the expression for the time period ( τ ) of oscillation: τ = 2 π ω n Here, ω n is the natural circular frequency. Rewrite the above equation, ω n = 2 π τ (1) Calculate the natural circular ( ω n ) frequency: Substitute 0.5 s for τ in equation (1) 0.5 s = 2 π ω n ω n = 2 π 0.5 ω n = 4 π rad / s The end C is pulled for 1.5 in. and released (b) To determine The centroidal radius of gyration ( k ¯ ) of the flywheel.

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

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

Publisher: McGraw-Hill Education

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

Question

Chapter 19.2, Problem 19.38P

(a)

To determine

The maximum angular velocity (θ˙m) of the flywheel.

(b)

To determine

The centroidal radius of gyration (k¯) of the flywheel.

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Chapter 19.2, Problem 19.37P

Chapter 19.2, Problem 19.39P

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The maximum angular velocity ( θ ˙ m ) of the flywheel.

Solution Summary: The author shows the free-body-diagram equation as in Figure (1).

Concept explainers

The maximum angular velocity (θ˙m) of the flywheel.

The centroidal radius of gyration (k¯) of the flywheel.

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Chapter 19 Solutions