Explanation Given information: The mass of the motor is M . The equivalent spring constant is k . The mass of the unbalance rotor is m . The forced circular frequency ( ω f ) is k M . Calculation: The expression for the natural circular frequency ( ω n ) : ω n = k M ω n 2 = k M k = ω n 2 M The expression for the rotating unbalanced mass is equivalent to an applied force as follows: P m = m r ω f 2 Calculate the amplitude of the forced vibration ( x m ) using the formula: x m = P m k 1 − ω f 2 ω n 2 Substitute m r ω f 2 for P m and ω n 2 M for k

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ISBN: 9781260804638

Author: BEER

Publisher: MCG

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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 19.113P

To determine

Show that when the angular velocity of the motor is (ωf) the amplitude (xm) of the motion of the motor.

xm=r(mM)(ωfωn)21−(ωfωn)2

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Chapter 19.4, Problem 19.112P

Chapter 19.4, Problem 19.114P

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Show that when the angular velocity of the motor is ( ω f ) the amplitude ( x m ) of the motion of the motor. x m = r ( m M ) ( ω f ω n ) 2 1 − ( ω f ω n ) 2

Solution Summary: The author explains that when the angular velocity of the motor is (omega

Concept explainers

Show that when the angular velocity of the motor is (ωf) the amplitude (xm) of the motion of the motor.

xm=r(mM)(ωfωn)21−(ωfωn)2

Want to see the full answer?

Chapter 19 Solutions

Show that when the angular velocity of the motor is ( ω f ) the amplitude ( x m ) of the motion of the motor. x m = r ( m M ) ( ω f ω n ) 2 1 − ( ω f ω n ) 2

Solution Summary: The author explains that when the angular velocity of the motor is (omega

Concept explainers

Show that when the angular velocity of the motor is (ωf) the amplitude (xm) of the motion of the motor. xm=r(mM)(ωfωn)21−(ωfωn)2

Want to see the full answer?

Chapter 19 Solutions

Show that when the angular velocity of the motor is (ωf) the amplitude (xm) of the motion of the motor.

xm=r(mM)(ωfωn)21−(ωfωn)2