Concept explainers
(a)
Magnitude of maximum angular velocity of bar
Answer to Problem 19.107P
The maximum angular velocity of bar AB is
Explanation of Solution
Given:
Mass of attached sphere is
Spring constant is
Vertical deflection is
Maximum amplitude of deflection is
Frequency of rotation is
Concept used:
Draw the FBD for bar AB in equilibrium state.
After giving small deflection to bar AB, Draw FBD of bar AB
Draw the equivalent kinetic diagram for bar AB as.
Write the expression for displacement of point C in terms of angular displacement.
Here,
Write the expression for displacement of point B in terms of angular displacement.
Here,
Substitute
Take moment about point A for equilibrium position.
For static equilibrium substitute
Simplify the above expression.
Here,
Take moment about point A after giving the angular displacement.
Substitute
Substitute
Substitute
Substitute
Substitute
Rearrange the above expression as.
Here,
Write the standard equation of motion as.
Compare the coefficient of
Compare the coefficient of
Write the expression for maximum amplitude of force.
Here,
Write the expression for natural frequency of system.
Here,
Write the expression for the amplitude of vibration of sphere B.
Here,
Write the expression for magnitude of maximum angular velocity of bar AB.
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The maximum angular velocity of bar AB is
Conclusion:
Thus, the maximum angular velocity of bar AB is
(b)
Magnitude of maximum acceleration of sphere
Answer to Problem 19.107P
The maximum acceleration of sphere is
Explanation of Solution
Concept used:
Write the expression for maximum acceleration of sphere.
Here,
Calculation:
Substitute
The maximum acceleration of sphere is
Conclusion:
Thus, the maximum acceleration of sphere is
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Chapter 19 Solutions
Vector Mechanics For Engineers
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