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AP Physics 1 SHM MC 1984 1. If the mass of a simple pendulum is doubled but its length remains constant, its period is multiplied by a factor of (A) 4. 1 2 (B) 1 2 (C) 1 (D) 2 (E) 2 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 to each other 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 1988 8. 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 Questions 11-12: 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, xmin and xmax. The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. 11. 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 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 Mass on Spring (A) T 2 T 2 T 2 (B) (C) T T (D) T 2 T (E) T 2 T T 2 60. An object weighing 4 newtons swings on the end of a string as a simple pendulum. At the bottom of the swing, the tension in the string is 6 newtons. What is the magnitude of the centripetal acceleration of the object at the bottom of the swing? (A) 0 (B) 0.5 g (C) g (D) 1.5 g (E) 2.5 g 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 1993 3. An ideal spring obeys Hooke's law, F = -kx. A mass of 0.50 kilogram hung vertically from this spring stretches the spring 0.075 meter. The value of 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 9. When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position. which of the following is true of the values of its speed and the magnitude of the restoring force? Speed Restoring Force (A) Zero Maximum (B) Zero Zero (C) ½ maximum ½ maximum (D) Maximum ½ maximum (E) Maximum Zero 43. 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) 1 s (B) 2 s (C) 3 s (D) 4 s (E) None of the above, because the acceleration is constant 1998 8. The graph above represents the potential energy U as a function of displacement x for an object on the end of a spring oscillating in simple harmonic motion with amplitude x. Which of the following graphs represents the kinetic energy K of the object as a function of displacement x ? 38. 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 56. An object moves up and down the y-axis with an acceleration given as a function of time t by the expression a = A sin t, where A and are constants. What is the period of this motion? (A) (B) 2 (C) 2A (D) 2/ (E) /2