Chapter 15: Q8CQ (page 472)
Is it possible to have damped oscillations when a system is at resonance? Explain.
Yes
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An object of mass , hanging from a spring with a spring constant of, is set into an up-and down simple harmonic motion. What is the magnitude of the acceleration of the object when it is at its maximum displacement of ? (a)Zero (b) (c) (d)(e).
A pendulum bob is made from a sphere filled with water. What would happen to the frequency of vibration of this pendulum if there were a hole in the sphere that allowed the water to leak out slowly?
A bungee jumper steps off a bridge with a light bungee cord tied to her body and to the bridge. The unstretched length of the cord isrole="math" localid="1660198723821" . The jumper reaches the bottom of her motion role="math" localid="1660198746464" below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an role="math" localid="1660198763301" free fall and a role="math" localid="1660198776457" section of simple harmonic oscillation. (a) For the free-fall part, what is the appropriate analysis model to describe her motion? (b) For what time interval is she in free fall? (c) For the simple harmonic oscillation part of the plunge, is the system of the bungee jumper, the spring, and the Earth isolated or non- isolated? (d) From your response in part (c) find the spring constant of the bungee cord. (e) What is the location of the equilibrium point where the spring force balances the gravitational force exerted on the jumper? (f) What is the angular frequency of the oscillation? (g) What time interval is required for the cord to stretch by role="math" localid="1660198795390" ? (h) What is the total time interval for the entirerole="math" localid="1660198809416" drop?
The mass of the deuterium molecule () is twice that of the hydrogen molecule (). If the vibrational frequency of is , what is the vibrational frequency of ? Assume the “spring constant” of attracting forces is the same for the two molecules.
You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move down and find that it hangs at rest with the spring stretched by 15.0 cm. Next, you lift the block back up to the initial position and release it from rest with the spring unscratched. What maximum distance does it move down? (a) 7.5 cm (b) 15.0 cm (c) 30.0 cm (d) 60.0 cm (e) The distance cannot be determined without knowing the mass and spring constant.
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