Oscillations - AP Physics B 1984

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1 Oscillations - AP Physics B If the mass of a simple pendulum is doubled but its length remains constant, its period is multiplied by a factor of (A) 1 2 (B) (C) (D) 2 (E) 2 A block oscillates without friction on the end of a spring as shown above. The minimum and maximum lengths of the spring as it oscillates are, respectively, x min and x max. The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. 4. Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring? (A) The kinetic and potential energies are equal at all times. (B) The kinetic and potential energies are both constant. (C) The maximum potential energy is achieved when the mass passes through its equilibrium position. (D) The maximum kinetic energy and maximum potential energy are equal, but occur at different times. (E) The maximum kinetic energy occurs at maximum displacement of the mass from its equilibrium position. 12. When a mass is attached to a spring, the period of oscillation is approximately 2.0 seconds. When the mass attached to the spring is doubled, the period of oscillation is most nearly (A) 0.5 s (B) 1.0 s (C) 1.4 s (D) 2.0 s (E) 2.8 s Oscillations - AP Physics B The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10.0 m Which graph can represent the total mechanical energy of the block-spring system as a function of x? (A) A (B) B (C) C (D) D (E) E 12. Which graph can represent the kinetic energy of the block as a function of x? (A) A (B) B (C) C (D) D (E) E 1 of 10

2 44. An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring, also with period T. If the masses of both objects are doubled, what are the new values for the periods? Pendulum (A) T 2 2T (B) T 2T (C) 2T T (D) 2T T (E) 2T T 2 Mass on Spring 9. When an object oscillating in simp1e harmonic motion is at its maximum displacement from the equi1ibrium position, which of the following is true of the values of its speed and the magnitude of the restoring force? Speed (A) Zero (B) Zero (C) ½ maximum (D) Maximum (E) Maximum Restoring Force Maximum Zero ½ maximum ½ maximum Zero 69. An object is attached to a spring and oscillates with amplitude A and period T as represented on the graph above. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following? (A) v > 0, a > 0 (B) v > 0, a < 0 (C) v > 0, a = 0 (D) v = 0, a < 0 (E) v = 0, a = 0 Oscillations - AP Physics B A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram above. At what time t does the particle achieve its maximum positive acceleration? (A) 1s (B) 2s (C) 3s (D) 4s (E) None of the above, because the acceleration is constant 47. A block of mass m slides on a horizontal frictionless table with an initial speed v 0. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed from its natural length? 2 0 (A) v 2g (B) mg k (C) m k v 0 3. An ideal spring obeys Hooke's law, F = - kx. A mass of 0.50 kilogram hung vertically from this spring stretches the spring meter. The value or the force constant for the spring is most nearly (A) 0.33 N/m (B) 0.66 N/m (C) 6.6 N/m (D) 33 N/m (E) 66 N/m (D) (E) m k v 0 k m v 0 2 of 10

3 Oscillations - AP Physics B A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3.0 kg block is then replaced by a 4.0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4.0 kg block fall before its direction is reversed? (A) 9 cm (B) 18 cm (C) 24 cm (D) 32 cm (E) 48 cm Waves - AP Physics B A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning fork makes one complete vibration, the emitted wave travels (A) one wavelength (B) about 340 meters (C) a distance directly proportional to the frequency of the vibration (D) a distance directly proportional to the square root of the air density (E) a distance inversely proportional to the square root of the pressure Waves - AP Physics B Two wave pulses, each of wavelength, are traveling toward each other along a rope as shown above. When both pulses are in the region between points X and Y. which are a distance apart, the shape of the rope will be which of the following? 35. A small vibrating object S moves across the surface of a ripple tank producing the wave fronts shown above. The wave fronts move with speed v. The object is traveling in what direction and with what speed relative to the speed of the wave fronts produced? Direction Speed (A) To the right Equal to v (B) To the right Less than v (C) To the right Greater than v (D) To the left Less than v (E) To the left Greater than v 40. A cord of fixed length and uniform density, when held between two fixed points under tension T, vibrates with a fundamental frequency f. If the tension is doubled, the fundamental frequency is (A) 2f (B) (C) f (D) (E) f 2 f 2 f A train whistle has a frequency of 100 hertz as heard by the engineer on the train. Assume that the velocity of sound in air is 330 meters per second. If the train is approaching a stationary listener on a windless day at a velocity of 30 meters per second, the whistle frequency that the listener hears is most nearly (A) 90 Hz (B) 110Hz (C) 120 Hz (D) 240 Hz (E) 300 Hz 3 of 10

4 52. A radar operates at a wavelength of 3 centimeters. The frequency of these waves is 32. Two sinusoidal functions of time are combined to obtain the result shown in the figure above. Which of the following can best be explained by using this figure? (A) Beats (B) Doppler effect (C) Diffraction (D) Polarization (E) Simple harmonic motion Waves - AP Physics B 1993 (A) Hz (B) 10 6 Hz (C) 10 8 Hz (D) 3 x 10 8 Hz (E) Hz 58. In the Doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following? I. The speed of the source II. The speed of the observer III. The loudness of the sound (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. 27. The speed at which waves propagate on the string is 59. The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q. coincide? (A) 0.4 m/s (B) 2.5 m/s (C) 5 m/s (D) 10 m/s (E) 20 m/s 28. The fundamental frequency of vibration of the string is (A) I Hz (B) 2.5 Hz (C) 5 Hz (D) 7.5 Hz (E) 10 Hz 30. Sound in air can best be described as which of the following types of waves? (A) Longitudinal (B) Transverse (C) Torsional (D) Electromagnetic (E) Polarized 4 of 10

5 Waves - AP Physics B One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown above, and is reflected at the wall. Properties of the reflected pulse include which of the following? I. It has a greater speed than that of the incident pulse. II. It has a greater amplitude than that of the incident pulse. III. It is on the opposite side of the string from the incident pulse. 48. A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown above, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest? (A) A (B) B (C) C (D) D (E) It will be the same at all four points. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III 5 of 10

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10 1996 PHYSICS B MECHANICS 2. A spring that can be assumed to be ideal hangs from a stand, as shown above. (a) You wish to determine experimentally the spring constant k of the spring. i. What additional, commonly available equipment would you need? ii. What measurements would you make? iii. How would k be determined from these measurements? (b) Assume that the spring constant is determined to be 500 N/m. A 2.0-kg mass is attached to the lower end of the spring and released from rest. Determine the frequency of oscillation of the mass. (c) Suppose that the spring is now used in a spring scale that is limited to a maximum value of 25 N, but you would like to weigh an object of mass M that weighs more than 25 N. You must use commonly available equipment and the spring scale to determine the weight of the object without breaking the scale. i. Draw a clear diagram that shows one way that the equipment you choose could be used with the spring scale to determine the weight of the object. ii. Explain how you would make the determination. 10 of 10