Concept explainers
The amplitude of vibration should be expected when three collar are placed on the spring.
Answer to Problem 19.112P
The amplitude of vibration of the system with three collars in out-phase motion is
Explanation of Solution
Given:
Amplitude of vibration when 1 collar is on the spring is
Amplitude of vibration when 2 collar is on the spring is
Concept used:
Write the expression for amplitude of forced vibration.
Here,
Write the expression for natural circular frequency of system having mass
Here,
Write the expression for natural circular frequency of system having mass
Substitute
Here,
Write the expression for natural circular frequency of system having mass
Substitute
Here,
Substitute
Here,
Substitute
Substitute
Here,
Substitute
Substitute
Here,
Calculation:
In-Phase motion:
Substitute
Substitute
Divide equation (9) by equation (8).
Solve the above expression for
Substitute
Substitute
The amplitude of vibration of the system with three collars in in-phase motion is
Out-of phase motion:
Substitute
Divide Equation (10) by equation (8).
Solve the above expression for
Substitute
Substitute
The amplitude of vibration of the system with three collars in out-phase motion is
Conclusion:
Thus, the amplitude of vibration of the system with three collars in out-phase motion is
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Chapter 19 Solutions
Vector Mechanics For Engineers
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