Concept explainers
The minimum tension occur in each spring.
Answer to Problem 19.137P
The minimum tension occur in each spring is
Explanation of Solution
Given information:
The mass of the block
The figure illustrates the free positions and extreme position.
Figure-(1)
Write the balanced equation of spring force and weight.
Here, the mass of the block
Write the balanced equation of spring force and weight after cutting the cord.
Here, the elongation of spring after cutting the cord is
Write the expression of displacement of block
Here, the maximum amplitude is
Write the expression of initial displacement of block
Here, the displacement of block
Differentiate the Equation (III) with respect to time.
Substitute
Write the expression of natural frequency of vibration of block
Here, the natural frequency of vibrations is
Write the expression of damping factor.
Here, the damping factor is
Write the expression of damped frequency in terms of natural frequency.
The velocity of the block
Write the expression of time period of oscillations.
Here, the time period of oscillations is
Write the expression for minimum stretch.
Here, the minimum stretch in the spring is
Write the expression of minimum tension in the spring.
Here, the minimum tension in the spring is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Equate the Equations (XIII) and (XIV).
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The minimum tension occur in each spring is
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Chapter 19 Solutions
Vector Mechanics For Engineers
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