Harmonic Motion · CAPE Physics Unit 1

113 past-paper questions on Harmonic Motion, part of Oscillations and Waves, from every CAPE Physics Unit 1 paper on Quelpr.

1. Q191 mark · multiple choice· CAPE Physics Unit 1 · 2007 · Paper 1For a particle oscillating with simple harmonic motion in a vertical plane, which of the following statements is NOT true?
2. Q281 mark · multiple choice· CAPE Physics Unit 1 · 2007 · Paper 1A particle oscillates so that its displacement x from a fixed point is related to time t by the equation x = 3 \sin(5\pi t). If x is measured in \text{cm} and t is measured in \text{s}, we can deduce…
3. Q291 mark · multiple choice· CAPE Physics Unit 1 · 2007 · Paper 1A pendulum swings freely with a period of 1.0\text{ s} on the earth's surface where acceleration due to gravity is g. If the pendulum were to swing in another place where acceleration due to gravity is g', what…
4. Q301 mark · multiple choice· CAPE Physics Unit 1 · 2007 · Paper 1Which of the following statements are TRUE about resonance? I. It occurs at the highest frequency of the oscillating system. II. It causes a significant increase in the amplitude of oscillation. III. It occurs when the…
5. Q281 mark · multiple choice· CAPE Physics Unit 1 · 2007 (Specimen) · Paper 1Which of the following quantites does NOT remain constant when a particle moves in simple harmonic motion?
6. Q291 mark · multiple choice· CAPE Physics Unit 1 · 2007 (Specimen) · Paper 1Item 29 refers to the following diagram. A mass, m, is attached to a vertical helical spring and displaced a distance "A" from equilibrium as shown in the diagram. The mass is released so that it oscillates with…
7. Q301 mark · multiple choice· CAPE Physics Unit 1 · 2007 (Specimen) · Paper 1Item 30 refers to the following diagram. A mass m, undergoes horizontal simple harmonic motion under the action of two springs as shown. Its equation of motion is a = -\frac{2k}{m}x and its amplitude is A. What…
8. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2008 (Rest of Region) · Paper 1In a simple harmonic motion with amplitude A and period T, the maximum velocity is
9. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2008 (Rest of Region) · Paper 1A particle moves with simple harmonic motion in a straight line. Which of the following graphs BEST represents the way in which the force F acting on the particle depends on the displacement x?
10. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2008 (Rest of Region) · Paper 1A mass of 250\text{ g} hanging at the end of a spring of spring constant, k, makes 21 oscillations in 11 seconds. What would be the period if the system were taken to a planet where gravity was \frac{1}{4} of that…
11. Q191 mark · multiple choice· CAPE Physics Unit 1 · 2008 (Rest of Region) · Paper 1A child's swing of mass 10\text{ kg} is oscillating with simple harmonic motion where the maximum height reached is 0.5\text{ m} above the equilibrium position. The following table shows pairs of energy values…
12. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2008 (T&T) · Paper 1A pendulum is held at its highest point and then released. A suitable graph to show one cycle of this motion could be
13. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2008 (T&T) · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin 0.4\pi t The frequency of oscillation of the particle is
14. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2008 (T&T) · Paper 1The phenomenon of damping is NOT useful in
15. Q201 mark · multiple choice· CAPE Physics Unit 1 · 2008 (T&T) · Paper 1A pendulum starts its oscillation from Position A. The kinetic energy of the pendulum bob is MAXIMUM when the bob is at
16. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2009 · Paper 1A mass hanging from a spring with force constant k oscillates vertically with an amplitude A. The MAXIMUM velocity on the mass during this simple harmonic motion is
17. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2009 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8\sin 0.4\,\pi\,t The frequency of oscillation of the particle is
18. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2010 · Paper 1When a particle oscillates in a straight line with simple harmonic motion, the period of the oscillation is
19. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2010 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8\sin 0.4\pi t The frequency of oscillation of the particle is
20. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2010 · Paper 1The diagram shows a Barton pendulum system used to demonstrate resonance. Which pendulum would swing with the GREATEST amplitude when the driver O is pulled aside and released?
21. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2011 · Paper 1Which of the following graphs BEST represents the relationship between total energy, E_T, potential energy, E_P, kinetic energy, E_K, and displacement of a particle moving in a straight line with simple harmonic…
22. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2011 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin(0.4\pi t) where x is in metres and t in seconds. The frequency of oscillation of the particle is
23. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2011 · Paper 1Item 18 refers to the following information. A system made up of a light helical spring to which a small mass is attached, is forced to oscillate at different frequencies, f, in air. The response is shown in the…
24. Q191 mark · multiple choice· CAPE Physics Unit 1 · 2011 · Paper 1Item 19 refers to the following diagram. What is the relationship between the periods of A and B, T_A and T_B respectively, if the two springs are similar?
25. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2012 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin(0.4\pi t) The frequency of oscillation of the particle is
26. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2012 · Paper 1A pendulum is held at its highest point and then released. A suitable graph to show one cycle of this motion is
27. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2012 · Paper 1Which of the following graphs represents a body undergoing critical damping?
28. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2013 · Paper 1A pendulum is held at its highest point and then released. A suitable graph to show one cycle of this motion could be
29. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2013 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin(0.4\pi t) where x is in metres and t in seconds. The frequency of oscillation of the particle is
30. Q181 mark · multiple choice· CAPE Physics Unit 1 · 2013 · Paper 1A pendulum starts its oscillation from Position A. The kinetic energy of the pendulum bob is MAXIMUM when the bob is
31. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2014 · Paper 1Item 16 refers to the following diagram below which shows a mass, m, hanging from a spring with force constant, k, and oscillating vertically with amplitude A. The MAXIMUM velocity on the mass during this simple…
32. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2014 · Paper 1Item 17 refers to the following diagram. A pendulum starts its oscillation from Position P. The kinetic energy of the pendulum bob is MAXIMUM when the bob is
33. Q211 mark · multiple choice· CAPE Physics Unit 1 · 2014 · Paper 1Which of the following graphs represents a body undergoing critical damping?
34. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2015 · Paper 1A pendulum is held at its highest point and then released. A suitable graph to show one cycle of this motion could be
35. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2015 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin 0.4 \pi t. The frequency of oscillation of the particle is
36. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2016 · Paper 1The MAXIMUM velocity of the mass during this simple harmonic motion is
37. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2016 · Paper 1The conditions necessary for a body to undergo simple harmonic motion are such that the acceleration is always directed towards a fixed point and is
38. Q161 mark · multiple choice· CAPE Physics Unit 1 · 2017 · Paper 1Which of the following graphs BEST represents the relationship between total energy, E_T, potential energy, E_p, kinetic energy, E_k, and displacement of a particle moving in a straight line with simple harmonic…
39. Q171 mark · multiple choice· CAPE Physics Unit 1 · 2017 · Paper 1The displacement of a particle undergoing simple harmonic motion is given by x = 8 \sin (0.4\pi t), where x is in metres and t in seconds. The frequency of oscillation of the particle is
40. 2(b)2 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2State the two conditions necessary for simple harmonic motion (SHM).
41. 2(c)(i)4 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2Calculate the mass of the wooden block.
42. 2(c)(ii)3 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2Calculate the angular frequency of the oscillations.
43. 2(c)(iii)3 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2Calculate the maximum velocity of the wooden block.
44. 2(d)(i)5 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2The amplitude of oscillation decreases gradually by 0.2 cm with each oscillation. On the axes in Figure 4, sketch the first five oscillations.
45. 2(d)(ii)3 marks· CAPE Physics Unit 1 · May/June 2021 · Paper 2Identify the phenomenon depicted by the waveform sketched in (d)(i) and state two real-life situations where it occurs.
46. 2(a)2 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2State the TWO conditions that must be satisfied for the oscillatory motion of an object to be considered simple harmonic.
47. 2(b)(i)2 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2State what the symbols A and ω represent in the equation.
48. 2(b)(ii)4 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2On the grid provided in Figure 3, sketch THREE graphs to show how displacement, y, velocity, v, and acceleration, a, each vary with time, t, for an object undergoing SHM for ONE period of oscillation. Use the same time…
49. 2(c)(ii)3 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2Calculate the maximum kinetic energy of the mass if it is displaced a further 0.045 m.
50. 2(d)(i)4 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2On the grid provided in Figure 5, plot a graph of amplitude of vibration, y, against frequency, f. Draw a smooth curve through the points.
51. 2(d)(ii)3 marks· CAPE Physics Unit 1 · May/June 2023 · Paper 2Use your graph to determine the angular frequency of the wooden block when it is oscillating at maximum amplitude.
52. 2(b)(i)3 marks· CAPE Physics Unit 1 · May/June 2026 · Paper 2Calculate the period of the motion of the block.
53. 2(b)(ii)4 marks· CAPE Physics Unit 1 · May/June 2026 · Paper 2Deduce the amplitude of the oscillation and provide an explanation in terms of energy transformations in the oscillating spring-mass system.
54. 2(b)(iii)3 marks· CAPE Physics Unit 1 · May/June 2026 · Paper 2Calculate the maximum speed, vₘ, of the oscillating block and state the position of the block when its maximum speed is attained.
55. 2(b)(iv)3 marks· CAPE Physics Unit 1 · May/June 2026 · Paper 2Calculate the maximum acceleration, aₘ, of the oscillating block.
56. 2(a)1 mark· Physics · Unit 1 Q2 2(a)Write an expression for the period of oscillation, T, of the mass-spring system.
57. 2(a)5 marks· Physics · Unit 1 Q2 2(a)On the grid provided on page 6, plot a graph to show how the amplitude of the driven pendulum varies with its length.
58. 2(a)(i)1 mark· Physics · Unit 1 Q2 2(a)(i)Explain what is meant by 'periodic motion'.
59. 2(a)(i)4 marks· Physics · Unit 1 Q2 2(a)(i)Describe an experiment to investigate the effect of damping on the amplitude of a mass-spring system.
60. 2(a)(i)2 marks· Physics · Unit 1 Q2 2(a)(i)State TWO conditions that must be satisfied for simple harmonic motion to occur.
61. 2(a)(ii)2 marks· Physics · Unit 1 Q2 2(a)(ii)Explain what is meant by 'simple harmonic motion'.
62. 2(a)(ii)1 mark· Physics · Unit 1 Q2 2(a)(ii)What adjustments can you make to the experiment in order to investigate whether the damping is constant or not?
63. 2(a)(ii)3 marks· Physics · Unit 1 Q2 2(a)(ii)Calculate the maximum kinetic energy of the cube.
64. 2(a)(iii)2 marks· Physics · Unit 1 Q2 2(a)(iii)Explain why the cube loses contact with the plate.
65. 2(a)(iv)3 marks· Physics · Unit 1 Q2 2(a)(iv)Calculate the amplitude of oscillation at the instant the cube loses contact with the plate.
66. 2(b)2 marks· Physics · Unit 1 Q2 2(b)Use the graph to find the value of n.
67. 2(b)(i)5 marks· Physics · Unit 1 Q2 2(b)(i)On the grid provided on page 7, plot a graph of amplitude of vibration, y, against frequency, f.
68. 2(b)(i)3 marks· Physics · Unit 1 Q2 2(b)(i)Calculate the value of f₀.
69. 2(b)(i)4 marks· Physics · Unit 1 Q2 2(b)(i)On the grid provided in Figure 4 (page 9), plot a graph of amplitude of oscillation, y, against frequency, f.
70. 2(b)(ii)1 mark· Physics · Unit 1 Q2 2(b)(ii)What is the value of the natural frequency on the graph?
71. 2(b)(ii)1 mark· Physics · Unit 1 Q2 2(b)(ii)Use your graph to determine the angular frequency for the block when it is oscillating at maximum amplitude.
72. 2(b)(ii)a)2 marks· Physics · Unit 1 Q2 2(b)(ii)a)For the block oscillating at maximum amplitude, determine the angular frequency.
73. 2(b)(ii)b)1 mark· Physics · Unit 1 Q2 2(b)(ii)b)For the block oscillating at maximum amplitude, determine the period of oscillation.
74. 2(b)(iii)1 mark· Physics · Unit 1 Q2 2(b)(iii)What effect occurs at this position?
75. 2(c)2 marks· Physics · Unit 1 Q2 2(c)Use your value of n to find a.
76. 2(c)3 marks· Physics · Unit 1 Q2 2(c)Calculate the period and frequency of the heavy pendulum.
77. 2(c)3 marks· Physics · Unit 1 Q2 2(c)Calculate the spring constant, k, for ONE of the springs.
78. 2(c)(i)1 mark· Physics · Unit 1 Q2 2(c)(i)For this harbour, calculate the MINIMUM depth of the water.
79. 2(c)(ii)5 marks· Physics · Unit 1 Q2 2(c)(ii)Calculate the two values of t, (t₁ and t₂), for which the water is 11.5 m deep. (Give the answer in hours).
80. 2(c)(iii)1 mark· Physics · Unit 1 Q2 2(c)(iii)Calculate the length of time for EACH tide during which the depth of water is MORE than 11.5 metres.
81. 2(d)2 marks· Physics · Unit 1 Q2 2(d)Suggest an accurate means of determining the time period, T.
82. 2(d)1 mark· Physics · Unit 1 Q2 2(d)What is the resonant frequency of the light pendulum?
83. 2(d)(i)2 marks· Physics · Unit 1 Q2 2(d)(i)On your graph, draw a line to show the possible variation with frequency of the amplitude of the vibration of the combined mass.
84. 2(d)(ii)1 mark· Physics · Unit 1 Q2 2(d)(ii)Briefly describe ONE situation in which it is advantageous to use the phenomenon illustrated in this experiment.
85. 4(b)(ii)2 marks· Physics · Unit 1 Q4 4(b)(ii)Calculate the angular velocity of the gymnast at Q.
86. 4(d)(i)1 mark· Physics · Unit 1 Q4 4(d)(i)Calculate the maximum attainable speed of the particle.
87. 4(d)(ii)2 marks· Physics · Unit 1 Q4 4(d)(ii)Calculate the maximum energy attained by the particle.
88. 5(a)2 marks· Physics · Unit 1 Q5 5(a)Define the term 'simple harmonic motion' (SHM).
89. 5(b)2 marks· Physics · Unit 1 Q5 5(b)Write the mathematical expression relating acceleration, a, to displacement, x, in simple harmonic motion.
90. 5(c)3 marks· Physics · Unit 1 Q5 5(c)Describe the interchange of the kinetic energy and potential energy of an oscillating system during simple harmonic motion.
91. 5(e)(ii)2 marks· Physics · Unit 1 Q5 5(e)(ii)Determine the period of the resulting SHM.
92. 6(c)4 marks· Physics · Unit 1 Q6 6(c)Calculate the lengths at which a tuning fork of 280 Hz would produce resonance. Ignore end connections. (Speed of sound = 340 m s⁻¹)
93. 6(d)5 marks· Physics · Unit 1 Q6 6(d)Write down expressions for displacement and velocity of the water molecules with time. Hence, deduce an expression for the power due to the water waves in terms of f, ρ, A and v for a cross section of area 1 m².
94. 7(a)2 marks· Physics · Unit 1 Q7 7(a)Explain what is meant by mechanical resonance.
95. 7(a)(i)8 marks· Physics · Unit 1 Q7 7(a)(i)Define 'simple harmonic motion' (S.H.M.) and write down an expression relating acceleration to displacement in S.H.M.
96. 7(a)(i)8 marks· Physics · Unit 1 Q7 7(a)(i)With the aid of sketch graphs, give an account of the energy transformations which occur during one complete cycle of this system.
97. 7(a)(ii)8 marks· Physics · Unit 1 Q7 7(a)(ii)Explain why a damped oscillating system experiences a progressive decrease in its amplitude.
98. 7(a)(ii)1 mark· Physics · Unit 1 Q7 7(a)(ii)Show that the time period of oscillation, T, of a simple pendulum of length l and mass m is given by T = 2π√(l/g) where g is the acceleration due to gravity.
99. 7(b)6 marks· Physics · Unit 1 Q7 7(b)Describe TWO practical cases in which the resonance that occurs is desirable and TWO cases in which it is not. Explain how damping may be achieved in the undesirable cases.
100. 7(b)1 mark· Physics · Unit 1 Q7 7(b)Calculate:
101. 7(b)(i)6 marks· Physics · Unit 1 Q7 7(b)(i)Calculate the time period of oscillation for the pendulum.
102. 7(b)(i)12 marks· Physics · Unit 1 Q7 7(b)(i)the acceleration of the piston at the endpoint of the stroke.
103. 7(b)(ii)1 mark· Physics · Unit 1 Q7 7(b)(ii)If the car is now at rest, and the pendulum undergoes S.H.M, would its time period be shorter or longer than that calculated in 7 (b) (i)? Explain your answer.
104. 7(b)(ii)12 marks· Physics · Unit 1 Q7 7(b)(ii)the speed of the piston at the midpoint of the stroke.
105. 7(b)(iii)12 marks· Physics · Unit 1 Q7 7(b)(iii)the kinetic energy of the piston at the midpoint of the stroke.
106. 7(c)(i)12 marks· Physics · Unit 1 Q7 7(c)(i)Determine, T, for a leg which is 0.9 m long, if the centre of mass is mid-way along the leg.
107. 7(c)(i)6 marks· Physics · Unit 1 Q7 7(c)(i)Determine the angular frequency of this oscillation.
108. 7(c)(ii)1 mark· Physics · Unit 1 Q7 7(c)(ii)Determine the speed of walking (in km h⁻¹) which is most effortless, if the person takes steps that are 0.8 m long.
109. 7(c)(ii)1 mark· Physics · Unit 1 Q7 7(c)(ii)Find the period of this S.H.M.
110. 7(c)(iii)1 mark· Physics · Unit 1 Q7 7(c)(iii)Calculate the maximum acceleration of the leg during the walk.
111. 7(c)(iii)a)1 mark· Physics · Unit 1 Q7 7(c)(iii)a)Find at time t = 1.0 s the displacement.
112. 7(c)(iii)b)1 mark· Physics · Unit 1 Q7 7(c)(iii)b)Find at time t = 1.0 s the velocity.
113. 7(c)(iii)c)1 mark· Physics · Unit 1 Q7 7(c)(iii)c)Find at time t = 1.0 s the acceleration.