Concept explainers
(a)
The combined spring constant.
Answer to Problem 19.143P
The combined spring constant is
Explanation of Solution
Given information:
The weight of two counter rotating eccentric mass exciters is
Write the expression of mass of imbalanced weight.
Here, the imbalanced mass is the acceleration due to gravity is
Write the expression of mass of the system.
Here, the mass of the system is
Write the expression of the frequency of periodic force.
Here, the rotational speed is
Write the expression of phase difference between the amplitude of vibration and periodic force.
Here, the damping coefficient is
Calculation:
Substitute
Substitute
Substitute
Since, the phase difference between the amplitude of vibration and periodic force is
Hence,
Substitute
Conclusion:
The combined spring constant is
(b)
The damping factor.
Answer to Problem 19.143P
The damping factor is
Explanation of Solution
Given information:
Write the expression of amplitude of steady state response of the system.
Here, the frequency of periodic force is
Write the expression for the amplitude of applied force.
Here, the radius of rotating mass is
Write the expression of critical damping coefficient.
Here, the critical damping coefficient is
Write the expression of damping factor.
Here, the damping factor is
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The damping factor is
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Chapter 19 Solutions
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