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PHYSICS, M3 EQ-Bank 8

A group of students investigates resonance using a mechanical oscillator (e.g. a mass-spring system) driven by a motor that allows them to vary the driving frequency. They measure the amplitude of oscillation at different frequencies.

  1. Describe what happens to the amplitude of the oscillating system as the driving frequency approaches the natural frequency of the system.   (2 marks)
  1. Explain the relationship between driving frequency, natural frequency, and energy transfer in this system.   (2 marks)
Show Answers Only

a.    As the driving frequency approaches the natural frequency:

  • The amplitude of the oscillation increases significantly.
  • At exact resonance, the system reaches its maximum amplitude because the energy from the driver is transferred most efficiently. 

b.   Frequency and energy transfer:

  • When the driving frequency equals the natural frequency, the system experiences resonance, resulting in maximum energy transfer into the system.
  • At other frequencies, less energy is transferred, and the amplitude of motion is smaller.
  • This shows that energy transfer is most efficient when both frequencies match.
Show Worked Solution

a.    As the driving frequency approaches the natural frequency:

  • The amplitude of the oscillation increases significantly.
  • At exact resonance, the system reaches its maximum amplitude because the energy from the driver is transferred most efficiently. 

b.   Frequency and energy transfer:

  • When the driving frequency equals the natural frequency, the system experiences resonance, resulting in maximum energy transfer into the system.
  • At other frequencies, less energy is transferred, and the amplitude of motion is smaller.
  • This shows that energy transfer is most efficient when both frequencies match.