Concept explainers
(a)
To plot:
The graph of potential energy versus time for three full periods of motion.
Answer to Problem 51QAP
The plot of potential energy is as below:
Explanation of Solution
Given data:
The potential energy of a simple harmonic oscillator,
Calculation:
The equation of motion for a given simple harmonic oscillator is
The potential energy of a simple harmonic oscillator is given by
The plots of U ( t ) should look like those for
For simplicity, the vertical axis of the following plot is
Figure 1
Conclusion:
Thus, the plot of potential energy versus time for three full periods of motion is shown in Figure 1.
(b)
The expression for the velocity,
Answer to Problem 51QAP
The expression for the velocity is given by,
Explanation of Solution
Given data:
The potential energy of a simple harmonic oscillator,
Calculation:
The equation of motion for a given simple harmonic oscillator is
The velocity of this oscillator is given by Equation,
Conclusion:
Thus, expression for the velocity,
(c)
To plot:
The graph of Kinetic energy on the same graph where potential energy versus time is drawn.
Explanation of Solution
Given data:
The potential energy of a simple harmonic oscillator,
Calculation:
The equation of motion for a given simple harmonic oscillator is
The velocity of this oscillator is given by equation,
The potential energy of a simple harmonic oscillator is given by
And the kinetic energy is given by
The plots of U ( t ) and K ( t ) should look like those for
For simplicity, the vertical axis of the following plot is
Figure 2
Conclusion:
Thus, the plot of kinetic energy versus time and potential energy versus time is shown in Figure 2.
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Chapter 12 Solutions
COLLEGE PHYSICS
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