Simple harmonic motion and its equationsEdexcel A-Level Physics: Subtopic test

1. 1
   A trolley of mass 0.40 kg is attached to a horizontal spring of spring constant 25 N m⁻¹. The other end of the spring is fixed. The trolley is pulled 0.060 m from its equilibrium position along a frictionless track and released. It then oscillates with simple harmonic motion.

   (a)

   Which statement is the condition for the trolley to perform simple harmonic motion?

   [1 mark]

   • AIts acceleration is constant and directed towards the equilibrium position
   • BIts resultant force is proportional to its displacement from equilibrium and directed towards equilibrium
   • CIts resultant force is constant in magnitude and always directed away from equilibrium
   • DIts speed is proportional to its displacement from equilibrium

   (b)

   What is the period of oscillation of the trolley?

   [1 mark]

   • A0.13 s
   • B1.26 s
   • C49.7 s
   • D0.795 s

   (c)

   Calculate the maximum speed of the trolley.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A simple pendulum consists of a small dense bob on a light string. The distance from the pivot to the centre of the bob is 1.50 m. The bob is displaced through a small angle and released. The gravitational field strength is 9.81 N kg⁻¹.

   (a)

   The length of the string is increased to four times its original value. What happens to the period of the pendulum?

   [1 mark]

   • AIt halves
   • BIt quadruples
   • CIt doubles
   • DIt is unchanged

   (b)

   Which change would NOT alter the period of the pendulum for small oscillations?

   [1 mark]

   • AReplacing the bob with one of greater mass but the same size
   • BTaking the pendulum to the surface of the Moon
   • CShortening the string
   • DMoving the pendulum to a lift accelerating upwards

   (c)

   Calculate the period and the frequency of the pendulum.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A loudspeaker cone vibrates with simple harmonic motion. Its displacement x from the equilibrium position is given by x = A cos ωt, where the amplitude A is 0.12 m and the frequency is 2.5 Hz. Time t = 0 is when the cone is at its maximum positive displacement.

   (a)

   Calculate the angular frequency of the vibration and the displacement of the cone 0.050 s after t = 0.

   [3 marks]

   (b)

   Calculate the maximum speed and the maximum acceleration of the cone, and state where in the oscillation the maximum acceleration occurs.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student investigates two oscillating systems: a mass on a vertical spring, and a simple pendulum in which the distance from the pivot to the centre of the bob is 0.640 m. For the pendulum, the student times 20 complete oscillations with a stopwatch and records 32.1 s.

   (a)

   A mass m is hung from a vertical spring of spring constant k. Explain why the mass performs simple harmonic motion for small oscillations and derive an expression for its period.

   [6 marks]

   (b)

   Use the pendulum measurements to calculate a value for the gravitational field strength, and evaluate the student's method of timing 20 oscillations.

   [6 marks]

   Total for question 4: 12 marks

End of questions