Chapter 14: Oscillations

1. Chapter 14: Oscillations Section 14-1: Simple Harmonic Motion

2. If F is the force, x the displacement, and k a positive constant, for simple harmonic motion we must have F = �k / x2 F = k / x F = (k / x2)� F = �k x2 F = �k x

3. If F is the force, x the displacement, and k a positive constant, for simple harmonic motion we must have F = �k / x2 F = k / x F = (k / x2)� F = �k x2 F = �k x

4. Any body moving with simple harmonic motion is being acted on by a force that is constant. proportional to a sine or cosine function of the displacement. proportional to the inverse square of the displacement. directly proportional to the displacement. proportional to the square of the displacement.

5. Any body moving with simple harmonic motion is being acted on by a force that is constant. proportional to a sine or cosine function of the displacement. proportional to the inverse square of the displacement. directly proportional to the displacement. proportional to the square of the displacement.

6. When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object is at its highest point. is at its lowest point. is at the equilibrium point.

7. When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object is at its highest point. is at its lowest point. is at the equilibrium point.

8. The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle? 1 2 3 4 None of these is correct.

9. The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle? 1 2 3 4 None of these is correct.

10. The order, from highest to lowest, of the frequencies of the oscillatory systems shown in the figure is a, b, c b, a, c c, b, a c, a, b a, c, b

11. The order, from highest to lowest, of the frequencies of the oscillatory systems shown in the figure is a, b, c b, a, c c, b, a c, a, b a, c, b

12. The order, from shortest to longest, of the periods of the oscillatory systems shown in the figure is a, b, c b, a, c c, b, a c, a, b a, c, b

13. The order, from shortest to longest, of the periods of the oscillatory systems shown in the figure is a, b, c b, a, c c, b, a c, a, b a, c, b

14. A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm. When the mass is 2.0 cm from the equilibrium position, what fraction of its total energy is potential energy? one-quarter one-third one-half two-thirds three-quarters

15. A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm. When the mass is 2.0 cm from the equilibrium position, what fraction of its total energy is potential energy? one-quarter one-third one-half two-thirds three-quarters

16. When the compression of a spring is doubled, the potential energy stored in the spring is the same as before. doubled. tripled. increased by a factor of 8. increased by a factor of 4.

17. When the compression of a spring is doubled, the potential energy stored in the spring is the same as before. doubled. tripled. increased by a factor of 8. increased by a factor of 4.

18. The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of approximately 0.7 1.0 1.4 2.0 4.0

19. The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of approximately 0.7 1.0 1.4 2.0 4.0

20. If the amplitude of a simple harmonic oscillator is doubled, the total energy is unchanged. one-fourth as large. half as large. doubled. quadrupled.

21. If the amplitude of a simple harmonic oscillator is doubled, the total energy is unchanged. one-fourth as large. half as large. doubled. quadrupled.

22. Which of the following statements is true of a particle that is moving in simple harmonic motion? The momentum of the particle is constant. The kinetic energy of the particle is constant. The potential energy of the earth�particle system is constant. The acceleration of the particle is constant. The force the particle experiences is a negative restoring force.

23. Which of the following statements is true of a particle that is moving in simple harmonic motion? The momentum of the particle is constant. The kinetic energy of the particle is constant. The potential energy of the earth�particle system is constant. The acceleration of the particle is constant. The force the particle experiences is a negative restoring force.

24. A body moving in simple harmonic motion has maximum acceleration when it has maximum velocity. maximum kinetic energy. minimum potential energy. minimum kinetic energy. zero displacement.

25. A body moving in simple harmonic motion has maximum acceleration when it has maximum velocity. maximum kinetic energy. minimum potential energy. minimum kinetic energy. zero displacement.

26. The displacement in simple harmonic motion is a maximum when the acceleration is zero. velocity is a maximum. velocity is zero. kinetic energy is a maximum. potential energy is a minimum.

27. The displacement in simple harmonic motion is a maximum when the acceleration is zero. velocity is a maximum. velocity is zero. kinetic energy is a maximum. potential energy is a minimum.

28. In simple harmonic motion, the magnitude of the acceleration of a body is always directly proportional to its displacement. velocity. mass. potential energy. kinetic energy.

29. In simple harmonic motion, the magnitude of the acceleration of a body is always directly proportional to its displacement. velocity. mass. potential energy. kinetic energy.

30. The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?

31. The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?

32. A system consists of a mass vibrating on the end of a spring. The total mechanical energy of this system varies as a sine or cosine function. is maximum when the mass is at maximum displacement. is a maximum when the mass is at its equilibrium position. is constant, regardless of the displacement of the mass from the equilibrium position. is always equal to the square of the amplitude.

33. A system consists of a mass vibrating on the end of a spring. The total mechanical energy of this system varies as a sine or cosine function. is maximum when the mass is at maximum displacement. is a maximum when the mass is at its equilibrium position. is constant, regardless of the displacement of the mass from the equilibrium position. is always equal to the square of the amplitude.

34. A body on a spring is vibrating in simple harmonic motion about an equilibrium position indicated by the dashed line. Which figure shows the body with maximum acceleration?

35. A body on a spring is vibrating in simple harmonic motion about an equilibrium position indicated by the dashed line. Which figure shows the body with maximum acceleration?

36. The mass on the end of the spring is in equilibrium, as shown. It is pulled down so that the pointer is opposite the 11-cm mark and then released. The mass experiences its maximum upward velocity at which of the following positions? 3-cm mark 7-cm mark 1-cm mark 11-cm mark None of these is correct.

37. The mass on the end of the spring is in equilibrium, as shown. It is pulled down so that the pointer is opposite the 11-cm mark and then released. The mass experiences its maximum upward velocity at which of the following positions? 3-cm mark 7-cm mark 1-cm mark 11-cm mark None of these is correct.

38. A mass of 2.00 kg suspended from a spring 100 cm long is pulled down 4.00 cm from its equilibrium position and released. The amplitude of vibration of the resulting simple harmonic motion is 4.00 cm 2.00 cm 8.00 cm 1.04 cm 1.02 cm

39. A mass of 2.00 kg suspended from a spring 100 cm long is pulled down 4.00 cm from its equilibrium position and released. The amplitude of vibration of the resulting simple harmonic motion is 4.00 cm 2.00 cm 8.00 cm 1.04 cm 1.02 cm

40. If the length of a simple pendulum with a period T is reduced to half of its original value, the new period T is approximately 0.5T 0.7T T (unchanged) 1.4T 2T

41. If the length of a simple pendulum with a period T is reduced to half of its original value, the new period T is approximately 0.5T 0.7T T (unchanged) 1.4T 2T

42. To double the period of a pendulum, the length must be increased by a factor of 2. must be decreased by a factor of 2. must be increased by a factor of 2�. must be increased by a factor of 4. need not be affected.

43. To double the period of a pendulum, the length must be increased by a factor of 2. must be decreased by a factor of 2. must be increased by a factor of 2�. must be increased by a factor of 4. need not be affected.

44. A clock keeps accurate time when the length of its simple pendulum is L. If the length of the pendulum is increased a small amount, which of the following is true? The clock will run slow. The clock will run fast. The clock will continue to keep accurate time.

45. A clock keeps accurate time when the length of its simple pendulum is L. If the length of the pendulum is increased a small amount, which of the following is true? The clock will run slow. The clock will run fast. The clock will continue to keep accurate time.

46. You have landed your spaceship on the moon and want to determine the acceleration due to gravity using a simple pendulum of length 1.0 m. If the period of this pendulum is 5.0 s, what is the value of g on the moon? 1.3 m/s2 1.6 m/s2 0.80 m/s2 0.63 m/s2 2.4 m/s2

47. You have landed your spaceship on the moon and want to determine the acceleration due to gravity using a simple pendulum of length 1.0 m. If the period of this pendulum is 5.0 s, what is the value of g on the moon? 1.3 m/s2 1.6 m/s2 0.80 m/s2 0.63 m/s2 2.4 m/s2

48. Which of the following statements concerning the motion of a simple pendulum is incorrect? The kinetic energy is a maximum when the displacement is a minimum. The acceleration is a maximum when the displacement is a maximum. The period is changed if the mass of the bob is doubled and the length of the pendulum is halved. The time interval between conditions of maximum potential energy is one period. The velocity is a maximum when the acceleration is a minimum.

49. Which of the following statements concerning the motion of a simple pendulum is incorrect? The kinetic energy is a maximum when the displacement is a minimum. The acceleration is a maximum when the displacement is a maximum. The period is changed if the mass of the bob is doubled and the length of the pendulum is halved. The time interval between conditions of maximum potential energy is one period. The velocity is a maximum when the acceleration is a minimum.

50. A simple pendulum has a mass of 10 kg. The length of the pendulum is 1.0 m. The work required to move the pendulum from its vertical position at rest to a horizontal position at rest is approximately 0 10 J 16 J 98 J 1.6 kJ

51. A simple pendulum has a mass of 10 kg. The length of the pendulum is 1.0 m. The work required to move the pendulum from its vertical position at rest to a horizontal position at rest is approximately 0 10 J 16 J 98 J 1.6 kJ