Simple harmonic motionAQA A-Level Physics: Subtopic test

1. 1
   A buoy bobs vertically in a regular swell with simple harmonic motion of amplitude 0.40 m and time period 5.0 s.

   (a)

   What is the angular frequency of the buoy's motion?

   [1 mark]

   • A0.20 rad s⁻¹
   • B0.63 rad s⁻¹
   • C31 rad s⁻¹
   • D1.3 rad s⁻¹

   (b)

   What is the maximum speed of the buoy?

   [1 mark]

   • A0.50 m s⁻¹
   • B0.080 m s⁻¹
   • C2.0 m s⁻¹
   • D0.25 m s⁻¹

   (c)

   Calculate the maximum acceleration of the buoy.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The cone of a loudspeaker moves backwards and forwards with simple harmonic motion at a frequency of 250 Hz and an amplitude of 0.50 mm. The cone is at its maximum positive displacement at t = 0.

   (a)

   What is the maximum acceleration of the cone?

   [1 mark]

   • A0.79 m s⁻²
   • B2.5 × 10⁶ m s⁻²
   • C1.2 × 10³ m s⁻²
   • D31 m s⁻²

   (b)

   What is the speed of the cone when its displacement is 0.30 mm?

   [1 mark]

   • A0.79 m s⁻¹
   • B0.63 m s⁻¹
   • C0.47 m s⁻¹
   • D0.92 m s⁻¹

   (c)

   Calculate the displacement of the cone at t = 0.50 ms.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle moves along a straight line with simple harmonic motion. Its displacement x, in metres, from its equilibrium position at time t, in seconds, is given by x = 0.060 cos(8.0πt).

   (a)

   Determine the amplitude, the frequency and the time period of the motion.

   [3 marks]

   (b)

   Calculate the speed and the magnitude of the acceleration of the particle when its displacement is 0.036 m.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A body oscillates with simple harmonic motion of amplitude 0.080 m and time period 0.50 s. A motion sensor records its displacement x and a computer plots x against t. The software then plots v against t by finding the gradient of the x–t graph, and a against t by finding the gradient of the v–t graph. At t = 0 the body is at its maximum positive displacement.

   (a)

   Describe the shapes of the v–t graph and the a–t graph for the first cycle, explaining how each follows from the gradient of the previous graph, and state the phase relationship between a and x.

   [6 marks]

   (b)

   Calculate the maximum speed and maximum acceleration of the body. Hence compare the speed and the acceleration when the displacement is half the amplitude with their maximum values, and comment on the difference.

   [6 marks]

   Total for question 4: 12 marks

End of questions