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Damping and resonance Cambridge International AS & A Level Physics revision

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In plain words

Push a swing once and it gradually dies away: friction is draining its energy. That is damping. But give it a little push at just the right moment on every swing and it climbs higher and higher. That is resonance, and it is why soldiers break step when they cross a bridge.

5 things to know

  1. A free oscillation happens at the system's own natural frequency, with no driving force. A forced oscillation is driven by a periodic force, and happens at the frequency of the driver.
  2. Damping: resistive forces take energy from an oscillator, so its amplitude falls. Light damping: the amplitude dies away gradually over many oscillations. Critical damping: the system returns to rest in the shortest possible time without oscillating. Heavy damping: it returns slowly, without oscillating.
  3. Resonance: the amplitude of a forced oscillation is greatest when the driving frequency equals the natural frequency. That is when energy is passed from the driver to the oscillator most effectively.
  4. More damping makes the resonance peak lower and broader.
  5. The energy removed by damping ends up as thermal energy. Ductile materials that deform plastically absorb energy and cut down the amplitude, which is used to protect buildings in earthquakes.

Tips and tricks

  • On a graph of amplitude against driving frequency, light damping gives a tall, sharp peak at the natural frequency.
  • Car suspension is close to critically damped, so the car settles quickly after a bump without bouncing.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Damping and resonance: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. When does resonance happen?
    • when the driving frequency equals the natural frequency (the answer)
    • when the driving frequency is zero
    • when there is heavy damping
    • when the amplitude is zero

    The driver then feeds energy in most effectively.

  2. What is critical damping?
    • damping that brings a system to rest in the shortest time without oscillating (the answer)
    • damping so heavy that the system never returns
    • damping so light that it has no effect
    • damping that increases the amplitude

    It is what a car's suspension aims for.

  3. What happens to the amplitude of a lightly damped oscillator over time?
    • It falls gradually. (the answer)
    • It stays the same.
    • It rises.
    • It falls to zero at once.

    Each oscillation loses a little energy.

  4. The damping on a driven oscillator is increased. What happens to its resonance peak?
    • It gets lower and broader. (the answer)
    • It gets taller and sharper.
    • It doesn't change.
    • It moves to a much higher frequency.

    More energy is removed on each cycle.

  5. At what frequency does a forced oscillation happen?
    • the frequency of the driving force (the answer)
    • the natural frequency of the system
    • twice the natural frequency
    • zero

    The system is made to follow the driver.

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