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Damping

Key idea: Describe damping as energy loss in oscillations, compare light/critical/heavy damping, and explain why critical damping is useful (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Compare light, critical and heavy damping and explain critical-damping applications.

1. Definitions (Must Know)

A. Damping

Damping is the loss of mechanical energy from an oscillating system due to resistive forces (e.g. friction, air resistance, internal friction).

As energy is dissipated, the amplitude decreases with time.

B. Light damping (underdamped)

The system continues to oscillate, crossing equilibrium repeatedly, but its amplitude decreases gradually.

C. Critical damping

The system returns to equilibrium in the shortest time without oscillating.

D. Heavy damping (overdamped)

The system returns to equilibrium slowly without oscillating.

Light, critical and heavy damping comparedThree displacement-time sketches. Light damping crosses equilibrium repeatedly with decreasing amplitude. Critical damping returns to equilibrium fastest without crossing it. Heavy damping also does not cross equilibrium but returns more slowly.Light dampingunderdampedrepeated crossingsCritical dampingfastest without overshootquickest settlingHeavy dampingoverdampedslower settlingxtime
Scroll diagram horizontally to read all labels.
Only light damping oscillates. Critical damping is the boundary case that returns to equilibrium fastest without overshoot; heavy damping is slower.

2. Key Ideas (What Earns Marks)

  • Damping transfers mechanical energy from the oscillator, usually to internal energy of the system and surroundings.
  • Light damping: oscillations continue, amplitude decreases.
  • Critical damping: fastest return to equilibrium with no oscillation.
  • Heavy damping: no oscillation, but slower return than critical damping.
Why critical damping is useful

Many measuring instruments and car suspensions aim for critical damping so they settle quickly without repeated overshoot.

3. Detailed Explanations

A. What damping does physically

Damping forces do negative work on the oscillator, transferring energy out of the mechanical energy stores (usually into internal energy/heat in the surroundings).

B. Comparing the three cases (what you should say in exams)

TypeWhat you observeKey point
Light (underdamped)crosses equilibrium repeatedly with decreasing amplitudeenergy is dissipated each cycle
Criticalno oscillationfastest settling
Heavy (overdamped)no oscillationslower than critical

4. Common Mistakes

  • Mixing up “critical” and “heavy” damping (both do not oscillate, but critical is faster).
  • Saying “damping means no energy” (energy exists; it is being dissipated).

5. Exam Tips

  • If the question says “settles quickly without oscillating”, the answer is critical damping.
  • If it says “oscillates but dies away”, it is light damping.
  • Give one application (car suspension, meter pointer) for explanation marks.

6. Worked Examples

Modelled example 1

Identify the damping type

Core

Problem

A meter pointer overshoots its correct value and oscillates about it with decreasing amplitude before coming to rest. Classify the damping and justify the choice.
Study the worked solution

  1. Identify the observed feature

    Method

    The pointer crosses equilibrium repeatedly while the amplitude decreases.

    Reason

    Repeated crossing distinguishes an underdamped response from critical or heavy damping.

    Working

    Oscillation continues, but successive excursions become smaller.

  2. Classify the regime

    Method

    This is light damping, or an underdamped response.

    Reason

    Damping dissipates mechanical energy gradually, so oscillations die away rather than stopping immediately.

    Working

    Classification: lightly damped.

Guided practice 2

Critical vs heavy damping

About 3 min

Problem

Two door closers return without oscillating, but closer A settles faster than closer B. Which is closer to critical damping?

Try this before viewing the solution

Closer to critical damping

Hints

Hint 1: compare settling times
Both responses are non-oscillatory; now use the defining speed distinction.
View solution step by step

  1. Apply the criterion

    Method

    Closer A is closer to critical damping.

    Reason

    Critical damping is the shortest return to equilibrium without oscillation.

    Working

    A settles faster while still avoiding overshoot.

  2. Classify the slower response

    Method

    Closer B is more heavily damped relative to the critical case.

    Reason

    Overdamping also avoids oscillation but lengthens the return.

    Working

    B’s slower settling is consistent with heavier damping.

Common misconception 3

Choosing damping for a car suspension

Find and correct the mistake

Learner claim

A learner says a car suspension should use the greatest possible damping because more damping always makes the car settle faster after a bump. Diagnose the claim and choose the intended regime.

Try this before viewing the solution

Best idealised regime

View solution step by step

  1. Reject unlimited damping

    Method

    Very heavy damping can make the response slow.

    Reason

    Overdamping resists motion so strongly that equilibrium is approached sluggishly.

    Working

    More damping beyond the critical value increases settling time.

  2. Choose the target

    Method

    Use critical damping in the idealised comparison.

    Reason

    It gives the fastest return without oscillation or repeated bounce.

    Working

    Desired response: critical damping.

Examiner practice 4

What happens to amplitude with time?

3 marks

Examination question

A lightly damped oscillator has decreasing amplitude. State what happens to its mechanical energy, identify where that energy is transferred, and link this to the amplitude change. [3 marks]

Try this before viewing the solution

View solution step by step

  1. State the energy change

    1 mark

    Method

    The oscillator’s total mechanical energy decreases.

    Reason

    Resistive forces do negative work on the oscillating system.

    Working

    Mechanical energy is not conserved within the oscillator.

  2. Identify the transfer

    1 mark

    Method

    Energy is transferred mainly to internal energy of the system and surroundings.

    Reason

    Friction and drag dissipate organised mechanical energy, commonly as heating.

    Working

    Mechanical energy → internal energy.

  3. Link to amplitude

    1 mark

    Method

    The amplitude decreases with time.

    Reason

    Smaller mechanical energy corresponds to smaller maximum displacement.

    Working

    Successive extrema move closer to equilibrium.

Challenge 5

Identifying the more damped system from response curves

Minimal support

Independent transfer

Two amplitude–driving-frequency curves describe systems with the same natural frequency. Curve 1 has a higher, sharper peak; curve 2 has a lower, broader peak. Identify the more damped system and justify using both features.

Try this before viewing the solution

Hints

Hint 1: compare height and width
Greater damping changes both the maximum response and how sharply frequency-selective the response is.
View solution step by step

  1. Use peak height

    Method

    Curve 2 is more heavily damped.

    Reason

    Greater energy dissipation limits the maximum steady response near resonance.

    Working

    Lower peak ⇒ greater damping.

  2. Use peak width

    Method

    The broader peak supports the same conclusion.

    Reason

    Greater damping makes the response less sharply concentrated near the natural frequency.

    Working

    Broader response ⇒ greater damping.

7. Mind Stretchers

Mind stretcher 1: Why is “no oscillation” not enough?Extension

Explain why “no oscillation” alone cannot tell you whether the system is critically or heavily damped.

Show Answer

Both critical and heavy damping return to equilibrium without oscillating. The difference is the time taken: critical damping returns in the shortest time, while heavy damping returns more slowly.

Mind stretcher 2: Why not make damping as large as possible?Extension

If heavy damping prevents overshoot, why don’t we always use very heavy damping in instruments/suspensions?

Show Answer

Very heavy damping makes the return to equilibrium slow. You avoid overshoot, but the system takes too long to settle, so it is not responsive (e.g. a car feels “sluggish” over bumps and an instrument takes too long to give a reading).

Critical damping is the best compromise: no oscillation and the fastest settling.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027