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SHM Springs 1. A mass oscillates with a period of 1.6 seconds when attached to a spring (k = 25 N/m.). What is the mass?

[1.6 kg]

2. What will be the period of a 3 kg mass oscillating on a spring with a k = 210 N/m? The frequency?

[0.75 s, 1.33 Hz]

3. A 5.4 kg mass oscillates with a frequency of 10 Hz. What is the period? What must be the spring constant?

[0.1 s, 21,300 N/m]

4. If k = 75 N/m and m = 0.35 kg. How far will the spring stretch? x

m

[4.5 cm]

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5. A 0.75 kg mass is placed on s spring and it stretches it 0.085 m.

A. What is the spring constant? [86 N/m] B. How much potential energy is stored in the spring? [0.31 J]

6. A 65 kg physics student is laying on a trampoline (acts like a spring). He/she is oscillating with a frequency of 0.75 Hz. What is the spring constant of the trampoline?

[1400 N/m]

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7. A 1.5 kg object is undergoing SHM with amplitude of 0.010 m and a frequency of 8.0 Hz.

A. What is the period of the object? [0.13 s] B. What is the spring constant of the system? [3800 N/m] C. What will be the maximum velocity of the object? [±0.5 m/s] D. How long will it take to travel from one end to the equilibrium position? [0.031 s]

[11.5 J] 8. A 2.5 kg mass on a spring (k = 350 N/m) oscillates with a maximum speed of 0.80 m/s.

A. What is the amplitude of the motion? [0.068 m] B. What is the period of the motion? [0.53 s] C. What will be the maximum energy of the system? [0.80 J]

9. What is the total energy of a 2.4 kg object that is oscillating between -0.075 m and +0.075 m at 6.5 Hz?

10. A 900 kg car strikes a huge spring traveling at 22 m/s and compresses it 5.0 m. A. What is the spring constant of the spring? [17,400 N/m] B. How long will the car be in contact with the spring? [0.713 s]

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11. An object undergoes SHM according to the following equation:

)t0.8cos()m30.0(x =

A. What is the object’s amplitude? [0.30 m] B. What is the object’s frequency? [1.27 Hz] C. What are the maximum velocity and acceleration of the object? [v = 2.4 m/s, a = 19 m/s2]

12. Use the graph to find: A. The period. [4 s] B. The ω. [1.57 rad/s] C. The maximum velocity of the object. [4.71 m/s] D. The spring constant if the object is 4.5 kg. [11.1 N/m]

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13. Use the graph to find:

A. The period. [0.8 s] B. The amplitude. [2.55 m] C. The maximum acceleration [157 m/s2] D. x when t = 4.3 s. [-1.8 m]

14. A mass m has an ω = 2.3 Hz when attached to spring that has a k = 65 N/m. What is m? How far will it stretch the spring if the mass is hung from the spring?

[m = 12.3 kg, x = 1.85 m]

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15. A 2.0 kg fish stretches a spring scale 3.5 cm. It is then pulled down another 1.0 cm and released. What will be the frequency

of the fish as it bobs up and down?

[2.7 Hz]

16. A mass m on a spring vibrates with a frequency of 2.0 Hz. When 0.75 kg is added to the mass the frequency becomes 1.4 Hz. What is the value of m? (hint: same k for both)

[m = 0.72 kg]

17. A physics student is standing on the end of a diving board and oscillates at 1.5 Hz. What is the maximum amplitude of the

end so he/she will never lose contact with the board?

[0.11 m]

18. A large block P oscillates on a frictionless surface with a frequency of 1.25 Hz. Block B is on top of P and the coefficient of friction between the blocks (μS) is 0.600. What is the maximum amplitude of the motion so the block B will not slip?

[0.095 m]

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19. The two blocks collide and stick together. What will be the period of the oscillation? What will be the amplitude?

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k = 125 N/m 5 m/s 3 kg 7 kg

[T = 1.78 s, A = 0.99 m]

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SHM Pendulums:

20. What is the period of the pendulum whose length is 0.75 m?

[1.7 s] 21. A pendulum has a frequency of 1.0 Hz. What must be the length of the pendulum?

[0.25 m]

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22. An astronaut takes a 1.5 m pendulum to the surface of Mars and observes it to have a period of 4.0 s. What is the value of g

on mars?

[3.7 m/s2]

23. Pendulum A has a period that is 20% more than pendulum B. Which pendulum has a greater length? How much longer is it?

[Pendulum A is 1.44 times longer]

24. Pendulum C has a period that is 30% less than pendulum D. Which pendulum has a greater length? How much longer is it?

[Pendulum D is 2.04 times longer]

25. A 4 m long pendulum on Earth is set in motion. A. What is its period? B. What will be the highest (above the center) it will go on either side if its velocity in the center is 2 m/s?

A. [4.01 s] B. [0.2 m]

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26. A ball of mass m is pulled to the side so it is 10.0 cm above an identical ball and released. When they collide they stick

together. A. What is the initial angle of the string (θ)? [32.2° or 0.562 rad] B. How long will it take until they collide? [0.404 s] C. After they collide, what is their velocity? [0.70 m/s] D. What maximum angle will the string make after they collide? [16.1°]

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θ 65 cm

10 cm

27. A 1.3 m pendulum oscillates so that when the bob is in the middle its velocity is 0.65 m/s.

A. What is the amplitude of the pendulum? B. What is the maximum angle that it will make to the vertical? C. What will be the highest distance it will travel above its lowest point?

A

B C

A. [0.24 m] B. [10.5º] C. [0.022 m]

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28. A 2.5 m long pendulum makes 5 complete swings (other side and back) in 16 s. What is the value of g where the pendulum

is located?

[9.6 m/s2]

29. The Burj Khalifa in Dubai is the tallest building in the world (828 m) What would be the period of a pendulum hung from its top?

[57.8 seconds]

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Wave Properties

30. What is the name of the following wave?

31. What are the names of waves that travel at the speed of light? Name as many as you can….

32. What are the names of the waves that need a medium to travel through?

33. What is the name of this wave?

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Wave Calculations

34. Sound wave, λ = 0.25 m find f

[1372 Hz] 35. Light wave, f = 950,000,000 Hz find λ

[0.32 m]

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36. A car horn beeping at 1250 Hz. Find its wavelength.

[0.27 m] 37. The police use radar that operates with a λ = 0.0050 m. What is its frequency?

[6x1010 Hz]

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38. Bats can hear sounds that are as high as 120,000 Hz. What is the wavelength of those waves?

[0.00286 m]

39. A certain water wave has a λ = 2.0 m and a frequency of 7.0 Hz. What is the velocity of the waves?

[14 m/s]

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40. A tuning fork vibrates 250 times in 2 seconds.

A. What is the frequency? [125 Hz] B. What will be the wavelength of the sound produced? [2.74 m]

41. A person on the beach sees waves that are 3.0 m apart approaching the shore. They hear the waves crash 30 times every 60 seconds. What is the frequency and velocity of the water waves?

[f = 0.5 Hz, v = 1.5 m/s]

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42. A radio tower emits signals at frequency of 103,500,000. What is the wavelength of the waves?

[2.9 m] 43. Sound travels at 5,100 m/s in aluminum. The bleachers at NP are 100 m long. How long will sound take to travel from one

end to the other in aluminum? In air?

[0.0196 s in Al, 0.292 s in Air]

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44. Determine the following for the wave shown below:

A. Amplitude [6 cm] B. Wavelength [8 m] C. If it’s a sound wave, calculate its frequency…[43 Hz]

45. Determine the following for a the wave shown below: A. Amplitude [3] B. Wavelength. [24 m] C. If its and electromagnetic wave, calculate its frequency. [1.25x107 Hz]

6 18 24 30 12

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46. The speed of sound waves in air is 343 m/s. The average human can detect sound waves whose frequencies are between 20.0

Hz and 20,000 Hz. Between what wavelengths can the human ear detect?

[17.2 m and 0.0172 m]

47. Which wave will travel faster? (same tension for both)

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48. Sketch what will happen after the wave reaches the free end…

49. Sketch what will happen after the wave reaches the fixed end….

50. Which wave will travels the slowest? Same string for both…

2 kg

10 kg

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51. Sketch the wave after it reaches the chain. Both in the string and the chain.

52. Sketch what will happen when: The waves meet, and after the waves meet.

Before Meet After

4 4

6 2

3 5

3 7

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53. Sketch the wave after it reaches the string. Both in the rope and the string.

54. A B C

Sketch after A Sketch after B

Sketch after C

55. Observe the following situation:

Free End A B Heavy

Rope String

A. The reflected pulse from point A will be __________.

B. The reflected pulse from point B will be __________.

56. A wire has a mass of 1.70 kg and a length of 15.0 m. Waves travel through the wire at 75.0 m/s. What is the tension in the wire?

[638 N]

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57. What is the linear density of a guitar’s string in order for it to produce one complete wave of length 1.10 m with frequency of

35 Hz? The tension string is 52 N.

[0.035 kg/m]

58. In the following situation the person at the bottom sends a pulse. How long will it take to reach the top person?

[0.904 s]

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Harmonics Strings and Tubes

59. The oscillator is operating at 35 Hz. What is the linear density of the string in the following?

0.8 m 1.5 kg

[0.075 kg/m]

60. A string that has a mass of 0.085 kg and a length of 1.5 m is under a tension of 650 N. A. What is the linear density of the string? B. What will be the velocity of a wave in the string? C. What will be the 5th harmonic frequency of the string?

A.[0.057 kg/m] B.[107 m/s] C.[178 Hz]

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61. A string that has a mass of 0.032 kg and a length of 0.95 m is under a tension of 775 N.

A. What is the linear density of the string? B. What will be the velocity of a wave in the string? C. What will be the 8th harmonic frequency of the string?

A.[0.0337 kg/m] B.[151 m/s] C.[639 Hz]

62. A 0.095 kg wire has a length of 2.0 m and its fundamental frequency is 57.4 Hz.

A. What must be the tension in the wire? B. What will be the 5th harmonic frequency of the wire?

A.[2500 N] B.[287 Hz]

63. A 0.065 kg wire has a length of 1.6 m and its fundamental frequency is 68.3 Hz.

A. What must be the tension in the wire? B. What will be the 5th harmonic frequency of the wire?

A.[1940 N] B.[342 Hz]

64. What must be the linear density of the string shown if it is oscillating at 95 Hz under a tension of 450 N.

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0.35 m

[0.102 kg/m]

65. A guitar string is 0.70 m long and is tuned to play a fundamental frequency of 330 Hz. How far from the end should a finger

be placed to play a frequency of 440 Hz?

[17.5 cm] 66. What must m be to produce: 1 loop? 2 loops? 5 loops?

DL = 0.00039 kg/m

Oscillator..f = 60 Hz [1.29 kg]

[0.322 kg] [0.0516 kg]

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67. Two violin strings are tuned to play at the same fundamental frequency, 294 Hz. The tension in one string is decreased by

2.0 %. What will be the new frequency?

[291 Hz]

68. Two wires are parallel, and one is directly above the other. Each has a length of 50.0 m and a mass per unit length of 0.020 kg/m. However, the tension in wire A is 600 N, and the tension in wire B is300 N. Transverse wave pulses are generated simultaneously, one at the left end of wire A and one at the right end of wire B. The pulses travel toward each other. How much time does it take until the pulses pass each other? A

B

[0.17 s]

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69. Sketch and calculate the λ and the f of the following:

0.95 m 3rd Harmonic

[λ = 0.63 m, f = 542 Hz] 0.45 m 3nd Harmonic

[λ = 0.60 m, f = 572 Hz]

70. Indicate the number of nodes (N) and antinodes (A) that the following will have:

A. 7th Harmonic of a string.

B. 15th Harmonic of an open-open tube.

C. 5th Harmonic of an open-closed tube.

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71. A tube with one end closed has a 3rd harmonic frequency of 214.4 Hz. What must be the length of the tube?

[1.2 m] 72. What harmonic (n) of tube open on both ends with a length of 0.35 m has a frequency of 1960 Hz?

[4th ]

73. What will happen to the fundamental frequency of sound made by a tube open on both ends if: A. The length is doubled? B. The length is halved? C. A cap is placed on one end?

A. [decreases by 2] B. [increases by 2] C. [decreases by 2]

74. Sketch and calculate the λ and the f of the following:

1.5 m 2rd Harmonic

[λ = 1.5 m, f = 229 Hz] 1.3 m 5th Harmonic

[λ = 1.04 m, f = 330 Hz]

75. Indicate the number of nodes (N) and antinodes (A) that the following will have:

A. 6th Harmonic of a string.

B. 12th Harmonic of an open-open tube.

C. 3th Harmonic of an open-closed tube.

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76. A tube with one end closed has a 3rd harmonic frequency of 350 Hz. What must be the length of the tube?

[0.74 m] 77. What pattern (n) of tube open on both ends with a length of 1.85 m has a frequency of 278.1 Hz?

[3rd ]