1. A pendulum oscillates back and forth between point A and C, with total mechanical energy (kinetic energy and relative potential energy) of E. When the pendulum is at position B, half way from the bottom of oscillation, which of the following would be accurate?

a. KE=0Eb. KE=.25Ec. KE=.5Ed. KE=.75Ee. KE=E

2. A pendulum oscillates through a small angle with amplitude Θ, with a period of T. If the same pendulum were to oscillate with amplitude Θ/2, the relative period of oscillation would be

a. T/4b. T/2c. Td. 2Te. 4T

3. A pendulum of length L oscillates back and forth 4 times in 12 seconds. If we increased the length of the pendulum to 4L. How many times would the pendulum oscillate back and forth in 12 seconds?

a. .5b. 1c. 2d. 8e. 16

4. The spring is compressed and released at the position shown (x=0). A force sensor, attached to the wall and the spring, reads force as a function of distance from position x. Only two readings are available. When the spring is at .3m away from the compressed position the force sensor reads -6N. When the spring is .8m away from the compressed position, the force sensor reads 9N. What is the amplitude of the motion of the spring motion in meters?

a. .3b. .5c. .6d. .7e. .9

5. A normal spring based oscillator has a maximum acceleration of 2m/s2 and a mass of 4Kg, in an environment without frictional forces. If the amplitude of motion is 8m, what is the maximum speed?

a. .5m/sb. 2m/sc. 4m/sd. 8m/se. 16m/s

6. Two springs of equal mass and dimensions are each dropped from some height H. Each spring bounces off the ground and back into the air without any damping. Spring 1 has a spring constant of k, and Spring 2 has a spring constant of 2k. The maximum compression distance of spring 1 will be ____________spring 2 during impact with the ground, and the maximum height after bouncing for spring 1 will be __________spring 2.

a. Less than, Less thanb. Less than, greater thanc. Greater than, Less than d. Greater than, Equal toe. Greater than, Greater than

7. Using the graph of acceleration as a function of time for a harmonic oscillator. What is the equation for the velocity of the harmonic oscillator as a function of time? (Assume the velocity at time 0 is 0)

a. V=.5sin(8t)b. V=4sin(2t)c. V=-12sin(2t)d. V=-.5sin(8t) e. V=-32sin(8t)

8. A guitar string is plucked and the wave oscillates with speed s, wavelength λ, and frequency f. If the tension of the string is increased the wavelength will _________ and the speed of the wave will__________

a. Decrease, increaseb. Decrease, stay the samec. Increase, increased. Stay the same, decreasee. Stay the same, increase

9. A spring has a mass M attached to it while in the relaxed position. The mass is then released and the spring is permitted to oscillate. Which graph best represents the amplitude of oscillation as a function of mass added?

10. Which of the varying pendulums has the smallest frequency of oscillation? Assume each pendulum has the same mass and the length of each pendulum is identical.

11. What is the net spring constant of the system shown?

a. 1N/mb. (11/18)N/mc. (18/11)N/md. 4N/me. 11N/m

12. A ball slides back and forth in frictionless wells in the presence of gravity between points –A and A, as shown. Which of the following motions of the ball would be closest to simple harmonic?

13. Considering the equation of a wave moving along a string as y=4sin(2x-8t), what is the speed of the wave?

a. .25b. .5c. 2d. 4e. 16

14. The power created by an speaker increases from 1watt to 10,000watts. If the observer initially hears a sound level of 50dB at 1 watt when at 2 meters, how far away do they have to go to hear the sound with the same intensity?

a. 16mb. 32mc. 64md. 100me. 200m

15. A sound emitter produces sound at a set frequency. The pitch of the sound for the observer will be lowest at _____________ and equivalent to the natural pitch at_____________

a. A, B and Cb. A, B and Dc. C, B and Cd. C, B and De. C, B and A

16. Two speakers are changed from a lower to a higher frequency of sound. Which of the following will create a similar effect on the fringes?

a. Increasing the distance between the speakersb. Increasing the temperature of the airc. Increasing the wavelength emitted soundd. (a-c)e. None of the above

17. A space ship hovers over a black hole with a very large mass, M1. The space ship is using thrusters to maintain its elevation (it is NOT rotating around the hole). A pendulum with a very light chord is allowed to oscillate. The Pendulum oscillates through small angle Θ, with length L, bob mass M2, at a distance of R from the center of the black hole.

a. Solve for period of oscillation in terms of given variables and fundamental constants (g is not a fundamental constant, since distance from the planet is appreciably changing) (2pts)

As the distance from the center of the hole, R, is changed, and the pendulum period is recorded with the data as shown.

b. Plot the graph of Period as a function of distance from the center of the black hole and determine the slope of the graph (3pts)

c. Determine the mass contained within the black hole if the pendulum has a length of 4m.

d. If the angle of release is 10o, what is the amplitude of oscillation, A? e. Give the velocity of oscillation as a function of time. The direction shown

is positive and the pendulum takes 2 seconds to get to equilibrium from the position shown.

18. A 1kg object moving at a speed of 6m/s collides and sticks to the spring-mass system shown. The front face where the 1Kg objects collides and the spring itself are of negligible mass. The second object, connected to the spring, has a mass of 2Kg and is free to move away from the wall. The entire system is frictionless. The spring behaves as a normal spring with a constant of 100N/m.

a. What is the maximum compression distance of the spring?

b. What is the period of oscillation of the system?

c. What is the velocity of the center of mass of the system after the 2kg object leaves the wall? Assume right is the positive direction, and the 1Kg mass remains stuck to the end of the spring opposite the 2kg mass.

d. What is the acceleration of the 2kg object as a function of time? Assume time zero is the moment the 2kg object starts to leave the wall.

e. Determine the maximum vibrational energy of the system.

19. A spring has a mass M attached to it while in the relaxed position. The mass is then released and the spring is permitted to oscillate. Which graph best represents the amplitude of oscillation as a function of mass added?

20. Which of the varying pendulums has the smallest frequency of oscillation? Assume each pendulum has the same mass and the length of each pendulum is identical.

21. What is the net spring constant of the system shown?

a. 1N/mb. (11/18)N/mc. (18/11)N/md. 4N/me. 11N/m

22. A pendulum oscillates back and forth between point A and C, with total mechanical energy (kinetic energy and relative potential energy) of E. When the pendulum is at position B, half way from the bottom of oscillation, which of the following would be accurate?

a. KE=0Eb. KE=.25Ec. KE=.5Ed. KE=.75Ee. KE=E

23. A pendulum oscillates through a small angle with amplitude Θ, with a period of T. If the same pendulum were to oscillate with amplitude Θ/2, the relative period of oscillation would be

a. T/4b. T/2c. Td. 2Te. 4T

24. A pendulum of length L oscillates back and forth 4 times in 12 seconds. If we increased the length of the pendulum to 4L. How many times would the pendulum oscillate back and forth in 12 seconds?

a. .5b. 1c. 2d. 8e. 16

25. The spring is compressed and released at the position shown (x=0). A force sensor, attached to the wall and the spring, reads force as a function of distance from position x. Only two readings are available. When the spring is at .3m away from the compressed position the force sensor reads -6N. When the spring is .8m away from the compressed position, the force sensor reads 9N. What is the amplitude of the motion of the spring motion in meters?

a. .3b. .5c. .6d. .7e. .9

26. A normal spring based oscillator has a maximum acceleration of 2m/s2 and a mass of 4Kg, in an environment without frictional forces. If the amplitude of motion is 8m, what is the maximum speed?

a. .5m/sb. 2m/sc. 4m/sd. 8m/se. 16m/s

27. Two springs of equal mass and dimensions are each dropped from some height H. Each spring bounces off the ground and back into the air without any damping. Spring 1 has a spring constant of k, and Spring 2 has a spring constant of 2k. The maximum compression distance of spring 1 will be ____________spring 2 during impact with the ground, and the maximum height after bouncing for spring 1 will be __________spring 2.

a. Less than, Less thanb. Less than, greater thanc. Greater than, Less than d. Greater than, Equal toe. Greater than, Greater than

28. Using the graph of acceleration as a function of time for a harmonic oscillator. What is the equation for the velocity of the harmonic oscillator as a function of time? (Assume the velocity at time 0 is 0)

a. V=.5sin(8t)b. V=4sin(2t)c. V=-12sin(2t)d. V=-.5sin(8t) e. V=-32sin(8t)

29. A guitar string is plucked and the wave oscillates with speed s, wavelength λ, and frequency f. If the tension of the string is increased the wavelength will _________ and the speed of the wave will__________

a. Decrease, increaseb. Decrease, stay the samec. Increase, increased. Stay the same, decreasee. Stay the same, increase

30. A ball slides back and forth in frictionless wells in the presence of gravity between points –A and A, as shown. Which of the following motions of the ball would be closest to simple harmonic?

31. Considering the equation of a wave moving along a string as y=4sin(2x-8t), what is the speed of the wave?

a. .25b. .5c. 2d. 4e. 16

32. The power created by an emitter increases from 1watt to 10,000watts. If the observer initially hears a sound level of 50dB at 1 watt when at 2 meters, how far away do they have to go to hear the sound with the same intensity?

a. 16mb. 32mc. 64md. 100me. 200m

33. A sound emitter produces sound at a set frequency. The pitch of the sound for the observer will be lowest at _____________ and equivalent to the natural pitch at_____________

a. A, B and Cb. A, B and Dc. C, B and Cd. C, B and De. C, B and A

34. Two speakers are changed from a lower to a higher frequency of sound. Which of the following will create a similar effect on the fringes?

a. Increasing the distance between the speakersb. Increasing the temperature of the airc. Increasing the wavelength emitted soundd. (a-c)e. None of the above

35. A space ship hovers over a black hole with a very large mass, M1. The space ship is using thrusters to maintain its elevation (it is NOT rotating around the hole). A pendulum with a very light chord is allowed to oscillate. The Pendulum oscillates through small angle Θ, with length L, bob mass M2, at a distance of R from the center of the black hole.

f. Solve for period of oscillation in terms of given variables and fundamental constants (g is not a fundamental constant, since distance from the planet is appreciably changing) (2pts)

As the distance from the center of the hole, R, is changed, and the pendulum period is recorded with the data as shown.

g. Plot the graph of Period as a function of distance from the center of the black hole and determine the slope of the graph (3pts)

h. Determine the mass contained within the black hole if the pendulum has a length of 4m.

i. If the angle of release is 10o, what is the amplitude of oscillation, A? j. Give the velocity of oscillation as a function of time. The direction shown

is positive and the pendulum takes 2 seconds to get to equilibrium from the position shown.

36. A 1kg object moving at a speed of 6m/s collides and sticks to the spring-mass system shown. The front face where the 1Kg objects collides and the spring itself are of negligible mass. The second object, connected to the spring, has a mass of 2Kg and is free to move away from the wall. The entire system is frictionless. The spring behaves as a normal spring with a constant of 100N/m.

a. What is the maximum compression distance of the spring?

b. What is the period of oscillation of the system?

c. What is the velocity of the center of mass of the system after the 2kg object leaves the wall? Assume right is the positive direction, and the 1Kg mass remains stuck to the end of the spring opposite the 2kg mass.

d. What is the acceleration of the 2kg object as a function of time? Assume time zero is the moment the 2kg object starts to leave the wall.

e. Determine the maximum vibrational energy of the system.