ism_ch13 - Chapter 13 Oscillations About Equilibrium...

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Chapter 13 Oscillations About Equilibrium Answers to Even-numbered Conceptual Questions 2. The person’s shadow undergoes periodic motion, with the same period as the period of the Ferris wheel’s rotation. In fact, if we take into account the connection between uniform circular motion and simple harmonic motion, we can say that the shadow exhibits simple harmonic motion as it moves back and forth on the ground. 4. The mass moves a distance 2 A in the time T /2; it moves a distance 3 A in the time 3 T /4. 6. The total energy of this system increases by factor of two. This follows because doubling the mass causes the kinetic energy to be doubled at all times. But the total energy of the system is equal to the maximum kinetic energy; therefore, the total energy is also doubled. 8. The object moves through a distance of 6 A in the time 3 T /2. Therefore, the amplitude of motion is 2 D . 10. Recall that the maximum speed of a mass on a spring is v max = ω A , where = k / m . It follows that the maximum kinetic energy is K max = 1 2 mv max 2 = 1 2 mkA 2 / m ( ) = 1 2 kA 2 . Note that the mass cancels in our final expression for the maximum kinetic energy. Therefore, the larger mass moves more slowly by just the right amount so that the kinetic energy is unchanged. 12. (a) The angular frequency is halved. (b) The frequency is halved. (c) The maximum speed is halved. (d) The maximum acceleration is reduced by a factor of 4. (e) The total mechanical energy is reduced by a factor of 4. 14. The constant A represents the amplitude of motion; the constant B is the angular frequency. Noting that the angular frequency is = 2 π f , we have that the frequency is f = /2 π= B π . 16. Recalling that f = 2 1 π k m , we see that adding a passenger (which increases the mass) results in a lower frequency of oscillation. 18. The period of a pendulum is independent of the mass of its bob. Therefore, the period should be unaffected. 20. The answer is (ii). The period of a pendulum, whether a physical pendulum or a simple pendulum, decreases with decreasing length. Therefore, a shorter person’s leg has a period that is less than a taller person’s leg. 22. A pendulum behaves the same in an elevator moving with constant speed as it does in an elevator at rest. Therefore, the period is still T in both cases (a) and (b). 24. A mass on a spring behaves the same in an elevator that moves with constant speed as it does in one that is at rest. Therefore, the period is still T in both cases (a) and (b). 272
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Physics: An Introduction Chapter 13: Oscillations About Equilibrium 26. The answer is (iii). Both blocks have the same period because they experience the same restoring force for a given displacement from equilibrium. 28. The answer is (i). The period of a pendulum depends inversely on the acceleration of gravity, as we see in Equation 13-20. On the Moon, the acceleration due to gravity is less than on the Earth, therefore the period of the pendulum is greater than T .
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ism_ch13 - Chapter 13 Oscillations About Equilibrium...

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