AP Physics Simple Harmonic Motion Practice Test Answers: E,C,E,B,A,C,C,B,D,E,E,E 13. (a) 132.4 N (b) 0.315 Hz, 1.83 m (c) 3.55 m/s (d) 222.6 N (e) 2.64 m 14. (a) 0.51 m (b) 2.2 Hz (c) 9.8 m/s2 (d) 0.51 m (e) 0.703 m/s Questions 1-2: A block on a horizontal frictionless plane is attached to spring, as shown below. The block oscillates on the x-axis with simple harmonic motion of amplitude A.

x=-A x=0 x=A

_____1. Which of the following statements about the block is correct? A. At x=0, its velocity is zero. B. At x=0, its acceleration is at a maximum. C. At x=A, its displacement is at a minimum. D. At x=A, its velocity is at a maximum. E. At x=A, its acceleration is maximum. _____2. Which of the following statements about energy is correct? A. The potential energy of the spring is at a maximum at x=0. B. The potential energy of the spring is at a minimum at x=A. C. The kinetic energy of the block is at a maximum at x=0. D. The kinetic energy of the block is at a maximum at x=A. E. The kinetic energy of the block always equals the potential energy of the spring. _____3. A particle moves in simple harmonic motion represented by the graph of its position Vs time shown below. Which of the following equations represents the velocity of the particle as a function of time?

A. v(t) = 2cos(πt/4)

B. v(t) = -1.6cos(πt/2) C. v(t) = -2.4sin(πt/4) D. v(t) = -2sin(πt/2) E. v(t) = 1.6cos(πt/4)

_____4. A simple pendulum consists of a 2.0 kg brass bob on a string about 0.5 m long. It has a period of about 1.42 sec. The pendulum would have a period of about 5 seconds if the A. string were replaced by one 25 m long. B. string were replaced by one 6.2 m long. C. bob were replaced by a 0.6 kg brass sphere. D. bob were replaced by a 7.0 kg brass sphere. E. bob was released from a 0.5 m height. _____5. A simple pendulum has a frequency of 0.2 Hz on Earth. It is brought to Mars where g is 38% of its value on Earth. What will be the pendulum’s frequency on Mars? A. 0.12 Hz. B. 0.2 Hz. C. 0.08 Hz. D. 0.52 Hz. E. 0.32 Hz. _____6. A 0.8 kg meter stick pivots back and forth about a point at its 30 cm mark as shown below. Its rotational inertia about its center is ml2/12. What is the frequency of its motion?

A. 1.6 Hz. B. 0.8 Hz. C. 0.6 Hz. D. 1.3 Hz. E. 0.4 Hz. _____7. A mass oscillates on a spring with an amplitude of 0.6 m. What is its displacement when 60% of its energy is potential? A. 0.36 m. B. 0.41 m. C. 0.46 m. D. 0.51 m. E. 0.56 m.

Questions 8-12: The position of a 0.6 kg mass in an oscillating mass-spring system is given by the equation: x = -1.4sin(8πt). x is in meters and t in seconds. _____8. The frequency of the oscillation of the mass is A. 2 Hz. B. 4 Hz. C. 8 Hz. D. 16 Hz. E. 25 Hz. ____9. The equation describing the velocity of the mass as a function of time is A. 25.1sin(8πt). B. -25.1cos(8πt). C. 35.2sin(8πt). D. -35.2cos(8πt). E. 35.2cos(8πt). ____10. The velocity of the mass at t = 0.2 sec is most nearly A. -35.1 m/s. B. 35.1 m/s. C. 1.3 m/s. D. 10.9 m/s. E. -10.9 m/s. _____11. The maximum kinetic energy of the mass is A. 2 J. B. 7.5 J. C. 10.6 J. D. 189J. E. 372 J. _____12. The magnitude of the maximum acceleration of the mass is A. 35.2 m/s2. B. 9.8 m/s2. C. 632 m/s2. D. 379 m/s2. E. 884 m/s2.

13.(10 Points) The simple pendulum shown below is initially held in place by a horizontal rope, making a 42 degree angle to the vertical. The mass of the pendulum is 15 kg, its length is 2.5m, and it is attached to a point that is 5.2 m above the floor. Answer the following questions about the pendulum.

! = 42"

L = 2.5 m

5.2 m

A

(a) Determine the tension in the horizontal rope. (b) The horizontal rope is cut from the pendulum and it starts to oscillate in simple harmonic motion. Determine the pendulum’s frequency and amplitude (in meters). (c) Determine the pendulum’s maximum velocity. (d) Find the tension in the pendulum’s string when it is at the lowest point in its swing. (e) The pendulum’s string is cut when it is at the lowest point in its swing, determine how far from point A, which is directly below where the pendulum was attached to the ceiling, the pendulum bob will land.

14.(10 Points) A 3 kg block is fastened to a vertical spring that has a spring constant of 800 N/m. A 1.2 kg block rests on top of the 3 kg block, as shown below.

3 kg

1.2 kg

k = 800 N/m

(a) When the blocks are at rest, how much is the spring compressed from its uncompressed length? (b) The blocks are now pushed down so that they oscillate. Determine the frequency of the oscillation. (c) Determine the magnitude of the acceleration that the blocks can attain and still remain in contact at all times. (d) How far can the spring be compressed beyond the compression found in part (a) without having he resulting motion causing the blocks to exceed the acceleration value in part (c)? (e) Determine the maximum speed of the blocks if the spring is compressed the distance found in part (d) and released.