CIE A Level Physics (9702) 2019-2021

Revision Notes

19.2.1 Damping


  • In practice, all oscillators eventually stop oscillating
    • Their amplitudes decrease rapidly, or gradually
  • This happens due to resistive forces, such friction or air resistance, which act in the opposite direction to the motion of an oscillator
  • Resistive forces acting on an oscillating simple harmonic system cause damping
    • These are known as damped oscillations
  • Damping is defined as:

The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system

  • Damping continues until the oscillator comes to rest at the equilibrium position
  • A key feature of simple harmonic motion is that the frequency of damped oscillations does not change as the amplitude decreases
    • For example, a child on a swing can oscillate back and forth once every second, but this time remains the same regardless of the amplitude

Exam Tip

Make sure not to confuse resistive force and restoring force:

  • Resistive force is what opposes the motion of the oscillator and causes damping
  • Restoring force is what brings the oscillator back to the equilibrium position

Types of Damping

  • There are three degrees of damping depending on how quickly the amplitude of the oscillations decrease:
    • Light damping
    • Critical damping
    • Heavy damping

Light Damping

  • When oscillations are lightly damped, the amplitude does not decrease linearly
    • It decays exponentially with time
  • When a lightly damped oscillator is displaced from the equilibrium, it will oscillate with gradually decreasing amplitude
    • For example, a swinging pendulum decreasing in amplitude until it comes to a stop
  • Key features of a displacement-time graph for a lightly damped system:
    • There are many oscillations represented by a sine or cosine curve with gradually decreasing amplitude over time
    • This is shown by the height of the curve decreasing in both the positive and negative displacement values
    • The amplitude decreases exponentially
    • The frequency of the oscillations remain constant, this means the time period of oscillations must stay the same and each peak and trough is equally spaced

Critical Damping

  • When a critically damped oscillator is displaced from the equilibrium, it will return to rest at its equilibrium position in the shortest possible time without oscillating
    • For example, car suspension systems prevent the car from oscillating after travelling over a bump in the road
  • Key features of a displacement-time graph for a critically damped system:
    • This system does not oscillate, meaning the displacement falls to 0 straight away
    • The graph has a fast decreasing gradient when the oscillator is first displaced until it reaches the x axis
    • When the oscillator reaches the equilibrium position (x = 0), the graph is a horizontal line at x = 0 for the remaining time

Heavy Damping

  • When a heavily damped oscillator is displaced from the equilibrium, it will take a long time to return to its equilibrium position without oscillating
  • The system returns to equilibrium more slowly than the critical damping case
    • For example, door dampers to prevent them slamming shut
  • Key features of a displacement-time graph for a heavily damped system:
    • There are no oscillations. This means the displacement does not pass 0
    • The graph has a slow decreasing gradient from when the oscillator is first displaced until it reaches the x axis
    • The oscillator reaches the equilibrium position (x = 0) after a long period of time, after which the graph remains a horizontal line for the remaining time

Worked example

Types_of_Damping_Worked_example_-_Types_of_Damping_Question, downloadable AS & A Level Physics revision notes

    • Ideally, the needle should not oscillate before settling
      • This means the scale should have either critical or heavy damping
    • Since the scale is read straight away after a weight is applied, ideally the needle should settle as quickly as possible
    • Heavy damping would mean the needle will take some time to settle on the scale
    • Therefore, critical damping should be applied to the weighing scale so the needle can settle as quickly as possible to read from the scale

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