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Theme C — Wave Behaviour

C.4.6 The Effect of Damping — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 32 of 37 1 quiz

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Lesson summary

C.4.6 The Effect of Damping — IB PHYSICS SL notes: Describe damping, classify light, critical and heavy damping, and explain how damping changes the resonance curve.Damping — the reduction in energy and amplitude of oscillations caused by resistive forces on the oscillating syste…

  • Resistive versus restoring force
  • Intended damping
  • Unwanted damping
  • Applications
  • Oscillating with decaying envelope
  • Fast non-oscillating fall

Part 1 of 9What damping is

1Damping
  • Damping the reduction in energy and amplitude of oscillations caused by resistive forces on the oscillating system
  • Resistive forces include air resistance, friction and internal friction in a material.
  • The mechanical energy becomes thermal energy of the surroundings.
2Effect
  • Effect in free oscillation the amplitude falls with time until the oscillator rests at equilibrium
3Frequency
  • Frequency it does not change as the amplitude decreases, so the period stays constant
  • For light damping any change in frequency is tiny.
4Resistive versus restoring force
  • Resistive versus restoring force a resistive force opposes the motion and causes damping,
    • whereas a restoring force brings the oscillator back to equilibrium
5Intended damping
  • Intended damping shock absorbers, door closers and building suspension
6Unwanted damping
  • Unwanted damping a swing slowing down

Part 2 of 9Light damping

Behaviour
  • Behaviour the system oscillates many times with gradually falling amplitude
Decay
  • Decay the amplitude decays exponentially, not linearly, and falls by a constant fraction each cycle
Graph
  • Graph a sine or cosine curve inside a decaying envelope
  • The peaks are equally spaced because the frequency stays constant.
  • The height falls on both the positive and negative sides.
Example
  • Example a pendulum swinging until it stops

Part 3 of 9Critical damping

Behaviour
  • Behaviour the system returns to equilibrium in the shortest possible time without oscillating
Graph
  • Graph the displacement falls quickly to zero without crossing the axis, then stays at x = 0
Applications
  • Applications car suspensions, measuring-instrument pointers and the needle of a weighing scale
  • Cars return to height without bouncing after a bump.
  • A weighing needle settles as fast as possible so the scale can be read.

Part 4 of 9Heavy damping

Behaviour
  • Behaviour the system returns to equilibrium slowly without oscillating
Graph
  • Graph the displacement creeps to zero more slowly than with critical damping and never crosses zero
Example
  • Example door dampers that stop doors slamming shut

Part 5 of 9Matching graphs to damping

1Oscillating with decaying envelope
  • Oscillating with decaying envelope light damping
2Fast non-oscillating fall
  • Fast non-oscillating fall critical damping
3Slow non-oscillating fall
  • Slow non-oscillating fall heavy damping
4Comparing curves
  • Comparing curves the one that takes longest to reach zero without oscillating has the most damping

Part 6 of 9Damping and resonance curves

Damping and resonance curves
Resonance curve
  • Resonance curve it plots the amplitude against the driving frequency and peaks at the natural frequency f0
  • Below f0 the amplitude rises, at f0 it is maximum and above f0 it falls.
Natural frequency
  • Natural frequency damping does not change f0
Effect of more damping on the peak
  • Effect of more damping on the peak the peak height decreases
Effect of more damping on the width
  • Effect of more damping on the width the peak broadens, so the system responds over a wider range of frequencies
Effect of heavy damping on the position
  • Effect of heavy damping on the position the peak moves slightly lower than f0
Overall
  • Overall damping reduces the sharpness of resonance and the amplitude at the resonant frequency
Low frequencies
  • Low frequencies the response is about the same for all curves, since the system simply follows a slowly changing force

Part 7 of 9Energy and damping

Energy and amplitude
  • Energy and amplitude energy in a lightly damped oscillator falls as the square of the amplitude
  • A 5% fall in amplitude per cycle is about a 10% fall in energy per cycle.
Steady resonance
  • Steady resonance the energy supplied by the driver per cycle equals the energy lost to damping per cycle
  • A larger damping force therefore limits the maximum amplitude.

Part 8 of 9Applications

Light damping uses
  • Light damping uses a quartz crystal or a radio tuning circuit needs a tall sharp peak to select one frequency
Heavy damping uses
  • Heavy damping uses tuned mass dampers in skyscrapers oscillate out of phase with the building to absorb wind energy
Loudspeakers
  • Loudspeakers the cone is damped so the sound stops promptly when the signal stops
Instruments
  • Instruments the vibrating element has low damping so notes are sustained
Sketching
  • Sketching draw several peaks on the same axes near f0, with the most damped lowest and widest, and label them

Part 9 of 9More from the specification

1Formation of Standing Waves on a String
  • A standing wave forms on a stretched string with fixed ends when two identical travelling waves of equal frequency and amplitude propagate in opposite directions and superimpose.
2Nodes, Antinodes, and Boundary Conditions
  • Standing waves feature nodes and antinodes (points of maximum displacement); for a string fixed at both ends, nodes exist at the boundaries and resonant wavelengths form discrete harmonics (λ_n = 2L / n).
    • (points of zero amplitude)
3Damping in Forced Oscillations
  • When an external periodic driver induces forced vibrations in an oscillating system, damping forces extract mechanical energy, lowering peak resonance amplitude and broadening the resonant frequency response curve.
4Forced oscillation
  • Oscillation caused by a periodic driving force
5Progressive wave
  • Wave that transfers energy without transferring matter.
6External force
  • Force from the surroundings.
7Harmonic
  • Resonant mode of a stationary wave, with frequency a whole-number multiple of the fundamental where allowed.
8Antinode
  • Point of maximum amplitude on a stationary wave.
9Boundary
  • Surface between two media at which waves are partially reflected
10Wavelength
  • Distance between a point on one wave and the same point on the next wave
11Stationary
  • Not moving.
12Length
  • Resistance is directly proportional to the length of a wire.
13Standing wave
  • A pattern formed by two identical waves travelling in opposite directions, with fixed nodes and antinodes.
14Boundary condition
  • Constraint at an edge fixing whether there is a node or antinode.

Key terms

TermMeaning
DampingEnergy loss from an oscillator by resistive forces.
Light dampingMany oscillations with slowly falling amplitude.
Critical dampingFastest return to equilibrium without oscillation.
Heavy dampingSlow return to equilibrium with no oscillation.
Resistive forceForce opposing the motion of an oscillator, causing damping.
Resonance curveGraph of amplitude against driving frequency.

Avoid these mistakes

1
Saying damping changes the natural frequency a lot — for light damping the change is tiny.
2
Believing critical damping is the heaviest damping — heavy damping is greater than critical.
3
Thinking damping raises the resonance peak — it lowers and broadens it.
4
Describing damped oscillations as having decreasing frequency — the amplitude falls while the period stays nearly constant.
5
Forgetting that the energy lost is converted to thermal energy, not destroyed.

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