Concept explainers
(a)
The amplitude of oscillation.
(a)
Explanation of Solution
Given:
Mass of object is
Linear damping constant is
Value of force constant is
Value of maximum force is
Angular frequency is
Formula used:
Write expression for amplitude of damped oscillation.
Here,
Substitute
Calculation:
Substitute
Conclusion:
The amplitude of oscillation is
(b)
The frequency at which resonance occurs.
(b)
Explanation of Solution
Given:
Mass of object is
Linear damping constant is
Value of force constant is
Value of maximum force is
Angular frequency is
Formula used:
Write expression for condition of resonance.
Substitute
Calculation:
Substitute
Conclusion:
Thus, the frequency at which resonance occurs is
(c)
The amplitude of oscillation at resonance.
(c)
Explanation of Solution
Given:
Mass of object is
Linear damping constant is
Value of force constant is
Value of maximum force is
Angular frequency is
Formula used:
Write expression for amplitude of damped oscillation.
Here,
Write expression for condition of resonance.
Substitute
Solve above expression.
Calculation:
Substitute
Conclusion:
Thus, the amplitude of oscillation at resonance is
(d)
The width of resonance curve.
(d)
Explanation of Solution
Given:
Mass of object is
Linear damping constant is
Value of force constant is
Value of maximum force is
Angular frequency is
Formula used:
Write expression for width of resonance curve.
Here,
Calculation:
Substitute
Conclusion:
Thus, the width of the resonance curve is
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Chapter 14 Solutions
Physics for Scientists and Engineers, Vol. 3
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