Concept explainers
(a)
The average power delivered by a driving force.
(a)
Explanation of Solution
Formula used:
Write the expression for average power delivered in driving an oscillator.
Here,
Calculation:
Write the expression for the force as a function of time.
Here,
Write the expression for the position of the oscillator.
Here,
Differentiate the above equation.
Substitute
Conclusion:
Thus,the average power delivered by a driving force is
(b)
The average power delivered by a driving force.
(b)
Explanation of Solution
Given:
Formula used:
Write the expression for average power delivered in driving an oscillator.
Here,
Calculation:
Write the expression for the force as a function of time.
Here,
Write the expression for the position of the oscillator.
Here,
Differentiate the above equation.
Substitute
Write the expression for
Substitute above value in equation (5).
Conclusion:
Thus, the average power delivered by a driving forceis
(c)
Average value of
(c)
Explanation of Solution
Given:
Formula used:
Calculate the average value of
Calculate the average value of
Calculation:
Write the expression for average power.
Substitute
Conclusion:
Thus, average power is
(d)
Use triangle to show that
(d)
Explanation of Solution
Introduction:
Draw the triangle to calculate the value using triangle law.
Use the above triangle to find
Conclusion:
Thus, the value of
(e)
Average power is
(e)
Explanation of Solution
Given:
Formula used:
Write the expression for
Rearrange above equation for the value of
Write the expression for average power.
Calculation:
Substitute
Substitute
Conclusion:
Thus, proved thatAverage power is
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Chapter 14 Solutions
Physics for Scientists and Engineers
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