Simple harmonic motionEdexcel International A Level Physics: Subtopic test

1. 1
   A trolley of mass 0.40 kg rests on a horizontal, frictionless track. It is attached to a fixed support by a spring that obeys Hooke's law, with spring constant 25 N m⁻¹. The trolley is pulled 6.0 cm from its equilibrium position and released.

   (a)

   Which statement gives the condition for simple harmonic motion?

   [1 mark]

   • AThe resultant force is constant in magnitude and always directed towards the equilibrium position
   • BThe resultant force is proportional to the displacement and directed away from the equilibrium position
   • CThe resultant force is proportional to the displacement from the equilibrium position and directed towards it
   • DThe resultant force is proportional to the square of the displacement and directed towards the equilibrium position

   (b)

   Which of the following would also be expected to show simple harmonic motion?

   [1 mark]

   • AA mass on a spring, oscillating with a small amplitude within the limit of proportionality
   • BA ball bouncing repeatedly on a hard floor
   • CA car moving at constant speed around a circular track
   • DA pendulum swung through an angle of 120°

   (c)

   Explain why the trolley moves with simple harmonic motion after it is released.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle oscillates with simple harmonic motion with an amplitude of 4.0 cm and a frequency of 2.5 Hz. At time t = 0 it is at its maximum positive displacement.

   (a)

   What is the angular frequency of the oscillation?

   [1 mark]

   • A0.40 rad s⁻¹
   • B15.7 rad s⁻¹
   • C7.9 rad s⁻¹
   • D2.5 rad s⁻¹

   (b)

   Which equation gives the displacement x, in metres, at time t, in seconds?

   [1 mark]

   • Ax = 0.040 sin 15.7t
   • Bx = 0.040 cos 2.5t
   • Cx = 15.7 cos 0.040t
   • Dx = 0.040 cos 15.7t

   (c)

   Calculate the maximum speed and the maximum magnitude of the acceleration of the particle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student compares the oscillations of a mass on a spring with those of a simple pendulum. The mass-spring system consists of a mass of 0.250 kg suspended from a spring of spring constant 40 N m⁻¹. Use g = 9.81 m s⁻².

   (a)

   Calculate the period and the frequency of oscillation of the mass-spring system.

   [3 marks]

   (b)

   The student wants a simple pendulum with the same period as this mass-spring system. Calculate the length of the pendulum. Then explain why quadrupling the mass on the spring doubles its period, whereas the period of a pendulum does not depend on the mass of the bob.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An oceanography team studies a buoy that bobs vertically in the sea with simple harmonic motion, with an amplitude of 0.60 m and a period of 5.0 s. At t = 0 the buoy is at the top of its motion. The team also tests the same ideas using a mass on a spring and a simple pendulum in the laboratory.

   (a)

   Calculate the displacement, velocity and acceleration of the buoy 1.0 s after the top of its motion. Take upward as positive.

   [6 marks]

   (b)

   Starting from F = −kx, show that the period of a mass-spring oscillator is T = 2π√(m/k), and explain why a simple pendulum behaves as a simple harmonic oscillator only for small angles.

   [6 marks]

   Total for question 4: 12 marks

End of questions