You may use your books and notes. Moreover, you are encouraged to freely discuss the questions..which doesn't mean copying answers.

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1 Section: Oscillations Take-Home Test You may use your books and notes. Moreover, you are encouraged to freely discuss the questions..which doesn't mean copying answers. 1. In simple harmonic motion, the restoring force must be proportional to the: amplitude frequency velocity displacement displacement squared 2. A particle oscillating in simple harmonic motion is: never in equilibrium because it is in motion never in equilibrium because there is a force in equilibrium at the ends of its path because its velocity is zero there in equilibrium at the center of its path because the acceleration is zero there in equilibrium at the ends of its path because the acceleration is zero there 3. An object is undergoing simple harmonic motion. Throughout one complete cycle it: has constant speed has varying amplitude has varying period has varying acceleration has varying mass 4. When a body executes simple harmonic motion, its acceleration at the ends of its path must be: zero less than g more than g suddenly changing in sign none of these 5. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its period is: 2 Hz 10 s 0.05 Hz 2 s 1

2 0.50 s 6. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is: 2 Hz 10 s 0.05 Hz 2 s 0.50 s 7. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its angular frequency is: 0.79 rad/s 1.57 rad/s 2.0 rad/s 6.3 rad/s 12.6 rad/s 8. Frequency f and angular frequency are related by f = f = 2 f = / f = /2 f = 2 / 9. A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are: 40 cm, 2 Hz 20 cm, 4 Hz 40 cm, 2 Hz 25 cm. 4 Hz 20 cm, 2 Hz 10. A weight suspended from an ideal spring oscillates up and down. If the amplitude of the oscillation is doubled, the period will: remain the same _ increase by a factor of 2 double halve _ decrease by a factor of 2 2

3 11. In simple harmonic motion, the magnitude of the acceleration is greatest when the: displacement is zero displacement is maximum velocity is maximum force is zero none of these 12. In simple harmonic motion, the displacement is maximum when the: acceleration is zero velocity is maximum velocity is zero kinetic energy is maximum momentum is maximum 13. In simple harmonic motion: the acceleration is greatest at the maximum displacement the velocity is greatest at the maximum displacement the period depends on the amplitude the acceleration is constant the acceleration is greatest at zero displacement 14. The amplitude and phase constant of an oscillator are determined by: the frequency the angular frequency the initial displacement alone the initial velocity alone both the initial displacement and velocity 15. The acceleration of a body executing simple harmonic motion leads the velocity by what phase? 0 /8 rad /4 rad /2 rad rad 16. The displacement of a mass oscillating on a spring is given by x(t) = x m cos( t + ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant is: 0 /2 radians radians 3

4 3 /2 radians 2 radians 17. A simple harmonic oscillator consists of a mass and spring (m, k). It oscillates as shown in (i) with period T. If the spring is cut in half and used with the same mass m, as shown in (ii), the period will be: 2T _ 2T _ T/ 2 T T/2 18. A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2 cos(50t) where x is in meters and t is in seconds. The spring constant of the spring is: 1 N/m 100 N/m 150 N/m 7500 N/m none of these 19. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the maximum speed of the block is: 0.06 m/s 0.17 m/s 0.24 m/s 4.9 m/s 6.9 m/s 20. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is: 0.13 m 0.18 m 3.7 m 4

5 5.2 m 13 m 21. A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is zero ÒA/4 _ ÒA/ 2 ÒA/2 anywhere between -A and +A 22. The period of a simple pendulum is 1 s on earth. When brought to a planet where g is one-tenth that on earth, its period becomes: 23. The amplitude of oscillation of a simple pendulum is increased from 1 to 4. Its maximum acceleration changes by a factor of: 1/4 1/ A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g and a is: 25. The rotational inertia of a uniform thin rod about its end is ML 2 /3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m and M = 200 gram, this rod will have the same period as a simple pendulum of length: 33 cm 50 cm 67 cm 100 cm 150 cm 26. Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be: an ellipse 5

6 a circle a parabola a hyperbola none of the above 27. A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be: half the natural frequency of the oscillator the same as the natural frequency of the oscillator twice the natural frequency of the oscillator unrelated to the natural frequency of the oscillator determined from the maximum speed desired 6

7 Answer Key Section: Oscillations Take-Home Test You may use your books and notes. Moreover, you are encouraged to freely discuss the questions..which doesn't mean copying answers. 1. D 2. D 3. D 4. E 5. E 6. A 7. E 8. D 9. B 10. A 11. B 12. C 13. A 14. E 15. D 16. B 17. C 18. D 7

8 19. E 20. B 21. C 22. d 23. D 24. b 25. C 26. A 27. B 8