plumiSimple harmonic motion (SHM): AQA A‑Level Physics questions
AQA A-Level Physics past-paper questions on 3.6.1.2 Simple harmonic motion (SHM), 2008–2025, with mark schemes and examiner’s reports where available.
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Q03.1
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All 58 questions on Simple harmonic motion (SHM), as a list
- June 2025, Paper 1, Q03.1 (4 marks): Draw, on Figure 4, a graph of acceleration against displacement for the system. Label each axis with a suitable unit and scale. [4 marks] Figure 4
- June 2025, Paper 1, Q03.2 (1 mark): Label, with a P, a point on your graph where the mass has 50% of its maximum kinetic energy. [1 mark]
- June 2025, Paper 1, Q25 (1 mark): A pendulum is oscillating with simple harmonic motion. Which row gives the momentum of the pendulum bob and its gravitational potential energy (GPE) when the ac
- June 2024, Paper 1, Q30 (1 mark): A body is in simple harmonic motion of amplitude 0.60 m and period 2π seconds. What is its speed when its displacement is 0.20 m? [1 mark] A 0.32 m s−1 B 0.57 m
- June 2023, Paper 1, Q06.1 (2 marks): Show that the pencil moves with simple harmonic motion. [2 marks]
- June 2023, Paper 1, Q06.2 (2 marks): The time period T of the vertical oscillations is given by = 2 l T g π The measured value of l in Figure 15 is 85 mm. The pencil is pushed down 5.0 mm and relea
- June 2023, Paper 1, Q31 (1 mark): A mass, attached to two springs, oscillates horizontally between P and Q. The motion of the system is simple harmonic. Which quantity has its magnitude at a min
- June 2022, Paper 1, Q05.6 (2 marks): A lamp is used to project shadow images of the block and pendulum bob on a screen. Both shadows appear to move with SHM across the screen. Figure 11 shows the i
- June 2022, Paper 1, Q31 (1 mark): A particle performs simple harmonic motion with a time period of 1.4 s and an amplitude of 12 mm. What is the maximum speed of the particle? [1 mark] A 8.6 mm s
- November 2021, Paper 1, Q31 (1 mark): A particle of mass m is oscillating with simple harmonic motion. The period of the oscillation is T and the amplitude is A. What is the maximum kinetic energy o
- November 2020, Paper 1, Q24 (1 mark): A particle of mass m undergoes simple harmonic motion with amplitude A and frequency f. What is the total energy of the particle? [1 mark] A 2πmfA2 B 2π2mf 2A2
- June 2019, Paper 1, Q06.1 (1 mark): State the time, in milliseconds, when P is moving at its maximum positive velocity. [1 mark] time = ms
- June 2019, Paper 1, Q06.2 (3 marks): Calculate the maximum acceleration of P. [3 marks] acceleration = m s–2
- June 2019, Paper 1, Q29 (1 mark): The graph shows the variation of displacement d with time t for a particle moving with simple harmonic motion of period T. Which graph shows the variation of ki
- June 2019, Paper 1, Q30 (1 mark): Two pendulums A and B oscillate with simple harmonic motion. The time period of A is 2.00 s and the time period of B is 1.98 s. A and B are released in phase. W
- June 2018, Paper 1, Q29 (1 mark): A body performs simple harmonic motion. What is the phase difference between the variation of displacement with time and the variation of acceleration with time
- June 2018, Paper 1, Q30 (1 mark): An object of mass 0.15 kg performs simple harmonic motion. It oscillates with amplitude 55 mm and frequency 0.80 Hz What is the maximum value of its kinetic ene
- June 2017, Paper 1, Q07.1 (4 marks): Deduce the spring constant k for spring A and the mass m suspended from it. [4 marks] k = N m–1 m = kg
- June 2017, Paper 1, Q32 (1 mark): The graph shows how the displacement of a particle performing simple harmonic motion varies with time. Which statement is not correct? [1 mark] A The speed of t
- Specimen, Paper 1, Q30 (1 mark): The frequency of a body moving with simple harmonic motion is doubled. If the amplitude remains the same which of the following is also doubled? [1 mark] A The
- Specimen, Paper 1, Q31 (1 mark): A particle oscillates with undamped simple harmonic motion. The acceleration of the particle [1 mark] A is always in the opposite direction to its velocity. B d
- June 2016, PHYA4 Section A (old spec), Q5 (1 mark): Which one of the following statements is true when an object performs simple harmonic motion about a central point? A The acceleration is always directed away f
- June 2016, PHYA4 Section A (old spec), Q6 (1 mark): The graph shows how velocity changes with time for a simple pendulum moving with simple harmonic motion. Which one of the following statements related to the mo
- June 2016, PHYA4 Section A (old spec), Q7 (1 mark): A mass hanging on the end of a spring undergoes vertical simple harmonic motion. At which point(s) is the magnitude of the resultant force on the mass a minimum
- June 2015, PHYA4 Section A (old spec), Q4 (1 mark): For a body performing simple harmonic motion, which one of the following statements is correct? A The maximum kinetic energy is directly proportional to the fre
- June 2015, PHYA4 Section A (old spec), Q5 (1 mark): Which one of the following graphs shows how the acceleration, a, of a body moving with simple harmonic motion varies with its displacement, x? A a x B a x C a x
- June 2015, PHYA4 Section A (old spec), Q6 (1 mark): A particle of mass 5.0 × 10–3 kg, moving with simple harmonic motion of amplitude 0.15 m, takes 47 s to make 50 oscillations. What is the maximum kinetic energy
- June 2014, PHYA4 Section A (old spec), Q7 (1 mark): Which line, A to D, in the table gives the amplitude and frequency of a body performing simple harmonic motion whose displacement x at time t is given by the eq
- June 2014, PHYA4 Section A (old spec), Q8 (1 mark): The tip of each prong of a tuning fork emitting a note of 320Hz vibrates in simple harmonic motion with an amplitude of 0.50mm. What is the speed of each tip wh
- June 2014, PHYA4 Section B (old spec), Q3(b)(ii) (2 marks): Sketch a graph on Figure 4 to show how the acceleration of the mass varies with time over a period of 1.2 s, starting with the mass at the highest point of its
- June 2014, PHYA4 Section B (old spec), Q3(c)(ii) (4 marks): The maximum kinetic energy of the oscillating object is 2.0 × 10–2 J. Show that the amplitude of the oscillations of the object is about 40mm. [4 marks]
- June 2013, PHYA4 Section A (old spec), Q8 (1 mark): A particle of mass m oscillates in a straight line with simple harmonic motion of constant amplitude. The total energy of the particle is E. What is the total e
- June 2013, PHYA4 Section B (old spec), Q1(a) (2 marks): A simple pendulum is given a small displacement from its equilibrium position and performs simple harmonic motion. State what is meant by simple harmonic motion
- June 2013, PHYA4 Section B (old spec), Q1(b)(ii) (2 marks): Calculate the acceleration of the bob of the simple pendulum when the displacement from the equilibrium position is 42mm. acceleration ms–2 (2 marks)
- January 2013, PHYA4 Section A (old spec), Q7 (1 mark): The graph shows the variation in displacement with time for an object moving with simple harmonic motion. What is the maximum acceleration of the object? A 0.02
- June 2012, PHYA4 Section A (old spec), Q7 (1 mark): A mass on the end of a spring undergoes vertical simple harmonic motion. At which point(s) is the magnitude of the resultant force on the mass a minimum? A at t
- January 2012, PHYA4 Section A (old spec), Q6 (1 mark): Which one of the following statements is true when an object performs simple harmonic motion about a central point O? A The acceleration is always directed away
- January 2012, PHYA4 Section A (old spec), Q7 (1 mark): A body executes simple harmonic motion. Which one of the graphs, A to D, best shows the relationship between the kinetic energy, Ek, of the body and its distanc
- January 2012, PHYA4 Section B (old spec), Q3(b)(ii) (3 marks): Use your answers from parts (a) and (b)(i) to show that the amplitude A, which is the distance from Q to R, is about 25m. (3 marks)
- January 2012, PHYA4 Section B (old spec), Q3(c) (2 marks): Explain why, when the student rises above point P, her motion is no longer simple harmonic.
- June 2011, PHYA4 Section A (old spec), Q7 (1 mark): The frequency of a body moving with simple harmonic motion is doubled. If the amplitude remains the same, which one of the following is also doubled? A the time
- June 2011, PHYA4 Section B (old spec), Q2(b)(i) (2 marks): The oscillating trolley performs simple harmonic motion. State the two conditions which have to be satisfied to show that a body performs simple harmonic motion
- June 2011, PHYA4 Section B (old spec), Q2(c)(ii) (1 mark): If the amplitude of vibration of the copper ion is 10–11m, estimate its maximum speed. answer = ms–1 (1 mark)
- June 2011, PHYA4 Section B (old spec), Q2(c)(iii) (1 mark): Estimate the maximum kinetic energy of the copper ion. answer = J (1 mark)
- January 2011, PHYA4 Section A (old spec), Q4 (1 mark): Which one of the following graphs shows how the acceleration, a, of a body moving with simple harmonic motion varies with its displacement, x? x a A x a B x a C
- January 2011, PHYA4 Section A (old spec), Q5 (1 mark): A body moves with simple harmonic motion of amplitude A and frequency . What is the magnitude of the acceleration when the body is at maximum displacement? A ze
- January 2011, PHYA4 Section A (old spec), Q6 (1 mark): An object oscillating in simple harmonic motion has a time period T. The first graph shows how its displacement varies with time. Which of the subsequent graphs
- June 2010, PHYA4 Section A (old spec), Q6 (1 mark): A body moves with simple harmonic motion of amplitude 0.90m and period 8.9s. What is the speed of the body when its displacement is 0.70m? A 0.11 ms–1 B 0.22 ms
- June 2010, PHYA4 Section A (old spec), Q7 (1 mark): Which graph, A to D, shows the variation of the kinetic energy, Ek, with displacement x for a particle performing simple harmonic motion? Ek 0 A x Ek 0 C x Ek 0
- January 2010, PHYA4 Section A (old spec), Q6 (1 mark): Which one of the following gives the phase difference between the particle velocity and the particle displacement in simple harmonic motion? A rad B rad C rad D
- January 2010, PHYA4 Section A (old spec), Q7 (1 mark): A mass M hangs in equilibrium on a spring. M is made to oscillate about the equilibrium position by pulling it down 10cm and releasing it. The time for M to tra
- January 2010, PHYA4 Section B (old spec), Q1(a) (2 marks): Describe the energy changes that take place as the bob of a simple pendulum makes one complete oscillation, starting at its maximum displacement. (2 marks)
- January 2010, PHYA4 Section B (old spec), Q1(c) (3 marks): Figure 2 On Figure 2 draw a graph to show how the kinetic energy of the girl varied with time during the first complete oscillation, starting at the time of her
- June 2008, PA04A (2008 spec), Q1 (2 marks): 1 Which one of the following statements concerning the acceleration of an object moving with simple harmonic motion is correct? A It is constant. B It is at a m
- June 2008, PA04B (2008 spec), Q1(b) (4 marks): 1 (b) In a further test of the model, the whole block is displaced vertically downwards with an initial displacement of 90 mm. The block is then released at tim
- January 2008, PA04A (2008 spec), Q1 (2 marks): 1 Which one of the following statements is true when an object performs simple harmonic motion about a central point O? A The acceleration is always directed aw
- January 2008, PA04A (2008 spec), Q2 (2 marks): 2 A body executes simple harmonic motion. Which one of the graphs, A to D, best shows the relationship between the kinetic energy, Ek, of the body and its dista
- January 2008, PA04A (2008 spec), Q3 (2 marks): 3 The displacement (in mm) of the vibrating cone of a large loudspeaker can be represented by the equation x = 10 cos (150t), where t is the time in s. Which li
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