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sm_pdf_chapter13 - Chapter 13 Vibrations and Waves Quick...

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Chapter 13 Vibrations and Waves Quick Quizzes 1. (d). To complete a full cycle of oscillation, the object must travel distance 2 A to position and then travel an additional distance 2 A returning to the original position at . x =− xA =+ A 2. (c). The force producing harmonic oscillation is always directed toward the equilibrium position, and hence, directed opposite to the displacement from equilibrium. The acceleration is in the direction of the force. Thus, it is also always directed opposite to the displacement from equilibrium. 3. (b). In simple harmonic motion, the force (and hence, the acceleration) is directly proportional to the displacement from equilibrium. Therefore, force and acceleration are both at a maximum when the displacement is a maximum. 4. (a). The period of an object-spring system is 2 m π = T . Thus, increasing the mass by a factor of 4 will double the period of oscillation. k 5. (c). The total energy of the oscillating system is equal to 2 1 2 kA , where A is the amplitude of oscillation. Since the object starts from rest at displacement A in both cases, it has the same amplitude of oscillation in both cases. 6. (d). The expressions for the total energy, maximum speed, and maximum acceleration are ( ) 2 1 max max 2 , , and Ek A v A k m a A k m == = where A is the amplitude. Thus, all are changed by a change in amplitude. The period of oscillation is 2 Tm = k and is unchanged by altering the amplitude. 7. (c), (b). An accelerating elevator is equivalent to a gravitational field. Thus, if the elevator is accelerating upward, this is equivalent to an increased effective gravitational field magnitude g , and the period will decrease. Similarly, if the elevator is accelerating downward, the effective value of g is reduced and the period increases. If the elevator moves with constant velocity, the period of the pendulum is the same as that in the stationary elevator. 465
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466 CHAPTER 13 8. (a). The clock will run slow . With a longer length, the period of the pendulum will increase. Thus, it will take longer to execute each swing, so that each second according to the clock will take longer than an actual second. 9. (b). Greater. The value of g on the Moon is about one-sixth the value of g on Earth, so the period of the pendulum on the moon will be greater than the period on Earth.
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Vibrations and Waves 467 Answers to Even Numbered Conceptual Questions 2. Each half-spring will have twice the spring constant of the full spring, as shown by the following argument. The force exerted by a spring is proportional to the separation of the coils as the spring is extended. Imagine that we extend a spring by a given distance and measure the distance between coils. We then cut the spring in half. If one of the half- springs is now extended by the same distance, the coils will be twice as far apart as they were for the complete spring. Thus, it takes twice as much force to stretch the half-spring, from which we conclude that the half-spring has a spring constant which is twice that of the complete spring.
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This note was uploaded on 04/08/2008 for the course PHY 101 taught by Professor Pralle during the Spring '08 term at SUNY Buffalo.

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sm_pdf_chapter13 - Chapter 13 Vibrations and Waves Quick...

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