40. Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N-s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one half the fractional rate at which the mechanical energy decreases.

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CENGAGE MINDTAP
hapter 15: Oscillatory Motion
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AA
40. Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the spring
constant is 100 N/m, and b = 0.100 N-s/m.
(a) Over what time interval does the amplitude drop to half its initial value?
(b) What If? Over what time interval does the mechanical energy drop to half its initial value?
(c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic
oscillator is one half the fractional rate at which the mechanical energy decreases.
41. s Review. A lobsterman's buoy is a solid wooden cylinder of radius r and mass M. It is weighted at
one end so that it floats upright in calm seawater, having density p. A passing shark tugs on the slack rope
mooring the buoy to a lobster trap, pulling the buoy down a distance from its equilibrium position and
releasing it.
(a) Show that the buoy will execute simple harmonic motion if the resistive effects of the water are
ignored.
(b) Determine the period of the oscillations.
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Transcribed Image Text:Om/static/nb/u/evo/index.html?elSBN=9781337699310&id=295720296&nbld=776900&snapshotid=776900& CENGAGE MINDTAP hapter 15: Oscillatory Motion E L HY L ☐ AA 40. Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N-s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one half the fractional rate at which the mechanical energy decreases. 41. s Review. A lobsterman's buoy is a solid wooden cylinder of radius r and mass M. It is weighted at one end so that it floats upright in calm seawater, having density p. A passing shark tugs on the slack rope mooring the buoy to a lobster trap, pulling the buoy down a distance from its equilibrium position and releasing it. (a) Show that the buoy will execute simple harmonic motion if the resistive effects of the water are ignored. (b) Determine the period of the oscillations. New Chrome av Q Search this course A 1
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