Free and forced oscillations and resonanceEdexcel International A Level Physics: Subtopic test

1. 1
   A student hangs a mass of 0.250 kg from a spring of spring constant 40 N m⁻¹. She pulls the mass down a short distance and releases it, so that it oscillates. She then attaches the top of the spring to a vibration generator whose frequency can be varied while its amplitude is kept constant.

   (a)

   Which statement describes the motion of the mass after it is released, before the vibration generator is used?

   [1 mark]

   • AIt oscillates at a frequency set by an external periodic force
   • BIt oscillates at a frequency that depends on how far it was pulled down
   • CIt oscillates freely at its natural frequency with no continuing periodic force
   • DIts amplitude increases with time

   (b)

   The frequency of the vibration generator is slowly increased from well below to well above the natural frequency of the system. How does the amplitude of the mass change?

   [1 mark]

   • AIt increases to a maximum near the natural frequency, then decreases
   • BIt decreases continuously
   • CIt stays constant
   • DIt increases continuously

   (c)

   Calculate the natural frequency of the mass–spring system.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A loose plastic panel in a car dashboard rattles violently when the engine speed reaches 3000 revolutions per minute, but hardly at all at other engine speeds. The engine vibrations act as a periodic driving force on the panel.

   (a)

   What is the frequency of the engine vibrations at 3000 revolutions per minute?

   [1 mark]

   • A3000 Hz
   • B314 Hz
   • C5.0 Hz
   • D50 Hz

   (b)

   Which statement best explains why the panel vibrates with a large amplitude at 3000 revolutions per minute?

   [1 mark]

   • AThe driving force is greatest at this engine speed
   • BThe driving frequency equals the natural frequency of the panel, so energy is transferred most efficiently to it
   • CThe panel has no damping at this engine speed
   • DThe natural frequency of the panel is much higher than the driving frequency

   (c)

   Suggest how the rattling of the panel could be reduced without changing its natural frequency.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A steel strip is clamped at one end and has a natural frequency of 12 Hz. A vibration generator drives the strip at constant driving amplitude, and the driving frequency is increased from 5 Hz to 20 Hz. The investigation is repeated after a large card has been fixed to the free end of the strip, which increases the air resistance on the strip.

   (a)

   Describe how the amplitude of oscillation of the strip varies as the driving frequency is increased from 5 Hz to 20 Hz, without the card.

   [3 marks]

   (b)

   Compare the response of the strip with the card fitted to the response without it, and explain the differences.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student determines the mass of an unknown object using resonance. A spring hangs from a vibration generator driven by a signal generator, and known masses of 0.100 kg to 0.400 kg are hung from the spring in turn. For each known mass she finds the resonant frequency f. A graph of 1/f² against mass for the known masses is a straight line through the origin with gradient 1.58 s² kg⁻¹. The unknown mass resonates at a frequency of 2.40 Hz.

   (a)

   Describe how the student should carry out the investigation to find the resonant frequency for each known mass, and how she should use the results to determine the unknown mass.

   [6 marks]

   (b)

   Use the data to calculate the spring constant and the unknown mass, and explain why the value of the unknown mass is likely to be reliable.

   [6 marks]

   Total for question 4: 12 marks

End of questions