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
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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
| Term | Meaning |
|---|---|
| Damping | Energy loss from an oscillator by resistive forces. |
| Light damping | Many oscillations with slowly falling amplitude. |
| Critical damping | Fastest return to equilibrium without oscillation. |
| Heavy damping | Slow return to equilibrium with no oscillation. |
| Resistive force | Force opposing the motion of an oscillator, causing damping. |
| Resonance curve | Graph 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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