Concept explainers
(a)
The amplitude of the motion of bob
Answer to Problem 19.110P
The amplitude of motion of bob is
Explanation of Solution
Given:
Mass of bob is
Length of pendulum is
Mass of collar is
The relation of displacement is
The maximum amplitude of displacement is
Frequency is
Concept used:
Draw the diagram for system as shown below:
As the bob has a small displacement, from the above figure,
Here,
Write the expression for the force balance in initial condition.
Here,
Write the expression for Newton’s Law of motion in x-direction.
Substitute
Here,
Substitute
Substitute
Write the general differential equation of motion.
Here,
Compare equation (3) and (2).
Write the expression for the amplitude of forces vibration.
Here,
Calculation:
Substitute
Substitute
The amplitude of motion of bob is
Conclusion:
Thus, the amplitude of motion of bob is
(b)
The periodic force that should be applied to the collar to maintain periodic motion.
Answer to Problem 19.110P
The periodic force required to maintain the motion of collar is
Explanation of Solution
Concept used:
Draw the FBD of collar as shown below:
In the above Figure
Write the expression for Newton’s Law of motion in x-direction.
Substitute
Substitute
Substitute
Write the relation for
Differentiate the above expression with respect to
Differentiate the above expression with respect to
Substitute
Simplify the above expression for
`
Calculation:
Substitute
The periodic force required to maintain the motion of collar is
Conclusion:
Thus, the periodic force required to maintain the motion of collar is
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Chapter 19 Solutions
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