(a) Explanation Given information: The weight of the motor ( W ) is 400 lb . The unbalanced weight ( w ) is 3 oz or 3 16 lb . The distance between the weight of rotor to axis of rotation ( r ) is 6in . or 0 .5ft . The fluctuating force ( F m ) is 0.2 lb . The speed of the motor ( ω f ) is 100 rpm . The acceleration due to gravity ( g ) is 32.2 ft/s 2 . Calculation: Convert the unit of speed of motor from rpm to rad/s: ω f = ( ω f ) rpm × 2 π 60 Here, ( ω f ) rpm is the speed of the motor in rpm. Substitute 100 rpm for ( ω f ) rpm . ω f = 100 × 2 π 60 = 10.472 rad/s Calculate the mass of the motor ( M ) using the formula: W = M g M = W g Substitute 400 lb for W and 32.2 ft/s 2 for g . M = 400 32.2 = 12.422 lb ⋅ s 2 /ft Calculate the unbalanced mass ( m ) using the formula: w = m g m = w g Substitute 3 16 lb for w and 32.2 ft/s 2 for g . m = 3 16 lb 32.2 = 0.005823 lb ⋅ s 2 /ft The expression for the rotating unbalanced mass is equivalent to an applied force ( P m ) as follows: P m = m r ω f 2 The expression for the motion of the system which is defined by the differential equation as follows: x m = P m k − M ω f 2 Substitute m r ω f 2 for P m . x m = m r ω f 2 k − M ω f 2 The expression for the transmitted force ( F m ) as follows: F m = k x m Substitute m r ω f 2 k − M ω f 2 for x m (b) To determine Find the amplitude of the fluctuation force ( | F m | ) exerted on the foundation when the motor is run at 200 rpm .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

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 19.4, Problem 19.118P

(a)

To determine

Find the maximum allowable spring constant (k) of the pad.

(b)

To determine

Find the amplitude of the fluctuation force (|Fm|) exerted on the foundation when the motor is run at 200rpm.

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Chapter 19.4, Problem 19.117P

Chapter 19.4, Problem 19.119P

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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 - Prob. 19.2P 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 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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Find the maximum allowable spring constant ( k ) of the pad.

Solution Summary: The author calculates the maximum allowable spring constant (k) of the pad using the formula: comega_f=100times

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Find the maximum allowable spring constant (k) of the pad.

Find the amplitude of the fluctuation force (|Fm|) exerted on the foundation when the motor is run at 200rpm.

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Chapter 19 Solutions