Explanation Given information: The mass of the motor ( M 1 ) before the plate is added is 180 kg . The mass of the rotor ( m ) is 28 g or 0 .028kg . The static deflection of the beam ( δ s t ) is 12 mm or 0 .012m . The distance between the weight of rotor to axis of rotation ( r ) is 150 mm or 0 .15m . The speed of the motor ( ω f ) is 300 rpm . The amplitude of vibration ( x m ) is less than − 60 μm or − 60 × 10 − 6 m . The acceleration due to gravity ( g ) is 9.81 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 300 rpm for ( ω f ) rpm . ω f = 300 × 2 π 60 = 31.416 rad/s Calculate the equivalent spring constant ( k ) using the formula: k = M 1 g δ s t Substitute 180 kg for M 1 , 9.81 ft/s 2 for g , and 0 .012m for δ s t . k = 180 × 9.81 0.012 = 147.15 × 10 3 N/m Calculate the natural frequency of the periodic force ( ω n ) using the formula: ω n = k M 2 Substitute 147.15 × 10 3 N/m for k . ω n = 147.15 × 10 3 N/m M 2 ω n 2 = 147.15 × 10 3 N/m M 2 Calculate the amplitude of motion ( x m ) using the formula: x m = ( r m M 2 ) ( ω f ω n ) 2 1 − ( ω f ω n ) 2 Substitute 0

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…

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Chapter 19.4, Problem 19.117P

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Find the required mass (ΔM) of the plate.

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Chapter 19.4, Problem 19.116P

Chapter 19.4, Problem 19.118P

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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 required mass ( Δ M ) of the plate.

Solution Summary: The author calculates the mass of the motor, the rotor, and the distance between the weight and axis of rotation.

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Find the required mass (ΔM) of the plate.

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Chapter 19 Solutions