Damping — OCR A-Level Physics
Test yourself on Damping with OCR A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Damping explained
A free oscillation occurs when a system oscillates at its natural frequency with no external periodic driving force, after being displaced and released.
Read the full explanation
Its amplitude stays constant only if damping is negligible; otherwise it decays. A forced oscillation occurs when a periodic external driving force is applied, so the system oscillates at the driving frequency rather than its natural frequency. The amplitude of a forced oscillation depends on how close the driving frequency is to the natural frequency. When they are equal, resonance occurs and amplitude reaches a maximum. Damping reduces the peak amplitude at resonance and broadens the resonance curve, shifting the peak slightly.
(b)
This row is a structural sub-heading in section 5.3.3 Damping, not a standalone assessed statement. It signals that the following sub-parts, (i) and (ii), carry the examinable content on damping. When reading the specification, treat (b) as an umbrella label: everything beneath it belongs to the same topic area and may be examined together. Your task is to work through each sub-part in turn, noting what must be understood and what practical work is expected. Do not memorise the letter itself or treat it as a fact to recall; instead use it to organise revision, linking the theory of damping to the observation of forced and damped oscillations.
(i) the effects of damping on an oscillatory system
Damping removes energy from an oscillatory system, so the amplitude of free oscillations decreases over time. Light damping gives a gradual decay with the period almost unchanged; heavy damping returns the system to equilibrium slowly without oscillation; critical damping returns it in the shortest time without overshoot. The energy lost per cycle depends on the damping, and the decay envelope of a lightly damped system falls exponentially. For example, a pendulum in air loses a small fraction of its energy each swing, so its amplitude shrinks slowly while its period stays close to the undamped value.
(ii) observe forced and damped oscillations for
This sub-part requires practical observation of forced and damped oscillations. You should set up a system that can be driven at a chosen frequency, such as a mass on a spring with a vibration generator, and record how the amplitude of the steady-state oscillation varies as the driving frequency changes. You should also observe how adding damping changes that response. Record the driving frequency and the resulting amplitude, plot an amplitude–frequency graph, and identify the resonant peak. Compare runs with different amounts of damping to see how the peak height and width change.
(c) resonance; natural frequency
Every oscillatory system has a natural frequency, the frequency at which it oscillates freely once displaced. Resonance occurs when a periodic driving force is applied at a frequency equal to the natural frequency, producing a maximum amplitude of the steady-state oscillation. The sharpness and height of the resonant peak depend on the damping: lighter damping gives a taller, narrower peak, while heavier damping gives a lower, broader one. For example, a mass on a spring driven at its natural frequency swings with maximum amplitude, and adding a damping vane reduces that maximum.
(d) amplitude-driving frequency graphs for forced oscillators
An amplitude–driving frequency graph plots the steady-state amplitude of a forced oscillator against the driving frequency, with one curve for each level of damping. At low damping the curve peaks sharply near the natural frequency, so the resonant amplitude is large; as damping increases the peak becomes lower and broader and shifts slightly below the natural frequency. Far from resonance the amplitude is small and all curves converge. To read such a graph, identify the natural frequency from the peak position, compare peak heights to judge relative damping, and note that a broader curve means the oscillator responds appreciably over a wider frequency range.
(e) practical examples of forced oscillations and resonance.
A forced oscillation occurs when a periodic driving force is applied to a system, which then oscillates at the driving frequency. Resonance is the large-amplitude response when that driving frequency is equal to the system's natural frequency. Practical examples include a child on a swing pushed at the natural frequency, Barton's pendulums where a driver pendulum excites others of the same length, a washing machine drum shaking violently at a specific spin speed, and a bridge or building responding to wind or earthquakes. In each case, identify the driver, the driven oscillator, the natural frequency and the damping that limits the maximum amplitude. Damping removes energy from the system, preventing the resonant amplitude from increasing indefinitely and slightly reducing the resonant frequency.
Your focus
- Distinguish between free and forced oscillations using the presence of a driving force and the frequency of oscillation.
- Explain resonance in terms of driving frequency matching natural frequency.
- Describe how damping affects the amplitude and shape of a resonance curve.
Show all 21 objectives
- Identify that (b) is a structural heading covering sub-parts (i) and (ii) rather than a standalone statement.
- Explain how the sub-parts under (b) together define the required coverage of damping in section 5.3.3.
- Plan revision that addresses both the effects of damping and the observation of forced and damped oscillations.
- Describe how damping affects the amplitude and period of an oscillatory system.
- Distinguish between light, heavy and critical damping in terms of displacement–time behaviour.
- Explain that damping removes energy from the system, usually to thermal stores, and relate this to the decay of amplitude.
- Carry out a practical observation of forced oscillations and record amplitude against driving frequency.
- Describe how changing the damping alters the amplitude–frequency response of the system.
- Identify the resonant peak on an amplitude–frequency graph and relate it to the natural frequency.
- Define natural frequency and resonance in the context of forced oscillations.
- Explain how the amplitude of a driven oscillator varies with driving frequency near resonance.
- Describe how damping affects the height and width of the resonant peak.
- Interpret amplitude–driving frequency graphs for forced oscillators.
- Relate peak height and width to the level of damping.
- Identify the natural frequency and the resonant driving frequency from a graph.
- Identify the driving force and driven oscillator in practical examples.
- Explain resonance in terms of driving frequency and natural frequency.
- Explain how damping limits resonant amplitude in real systems.
Damping exam tips
Marking Points
- A free oscillation has no external periodic driving force and occurs at the natural frequency of the system.
- A forced oscillation is driven by a periodic external force and oscillates at the driving frequency.
- Amplitude of a forced oscillation depends on the frequency difference between driving and natural frequencies.
- Resonance occurs when driving frequency equals natural frequency, giving maximum amplitude.
- Damping reduces the maximum amplitude at resonance and broadens the resonance curve.
- Examples include a pendulum swinging freely and a mass on a spring driven by a vibrating support.
- Damping is the removal of energy from an oscillatory system, usually transferred to thermal stores, so the amplitude of free oscillations decreases with time.
- Light damping produces a gradual exponential decay of amplitude while the period remains approximately constant.
- Heavy damping causes the system to return to equilibrium slowly, without completing oscillations.
- Critical damping returns the system to its equilibrium position in the shortest time without overshoot, and is the boundary between oscillatory and non-oscillatory behaviour.
- The rate of energy loss per cycle increases with the degree of damping, so the amplitude decay is faster for heavier damping.
- The natural frequency of a system is the frequency at which it oscillates freely after being displaced from equilibrium.
- Resonance occurs when the driving frequency equals the natural frequency, giving maximum amplitude of the steady-state oscillation.
- The amplitude of the driven oscillation depends on the difference between the driving frequency and the natural frequency.
- Increasing the damping lowers and broadens the resonant peak, while decreasing the damping makes the peak taller and narrower.
- At resonance, energy is transferred most efficiently from the driving source to the oscillating system.
- Steady-state amplitude is plotted on the vertical axis and driving frequency on the horizontal axis.
- The peak occurs at the driving frequency closest to the natural frequency of the oscillator.
- Reducing damping raises and narrows the resonant peak; increasing damping lowers and broadens it.
- At driving frequencies well away from resonance the amplitude is small and curves for different damping converge.
- The resonant peak shifts slightly to a driving frequency below the undamped natural frequency as damping increases.
- A forced oscillation requires an external periodic driving force acting on the oscillator.
- Resonance occurs when the driving frequency matches the natural frequency of the system.
- The steady-state amplitude depends on the driving frequency and on the damping present.
- Practical examples include a swing pushed in time, Barton's pendulums, a washing machine at a critical spin speed, and structures responding to wind or seismic waves.
- Damping controls the resonant amplitude and can be desirable, for example in car suspension or building design.
Examiner Tips
- 💡State clearly whether a driving force is present before classifying an oscillation as free or forced.
- 💡Link resonance to the condition driving frequency equals natural frequency, and mention damping when discussing amplitude.
- 💡Use a resonance curve to show how damping changes peak height and width.
- 💡Use the lettered structure of the specification as a revision checklist: tick off each sub-part only when you can explain it and, where required, carry out the practical work.
- 💡When a question refers to damping, decide first whether it is testing the effects of damping on an oscillatory system or the observation of forced and damped oscillations, then select the relevant knowledge.
- 💡Link your notes on damping to the wider oscillations topic so that definitions, graphs and practical methods are revised together rather than in isolation.
- 💡Sketch the displacement–time graph for light, heavy and critical damping side by side so you can recognise and describe each case quickly.
- 💡When explaining energy loss, state where the energy goes, for example to thermal stores, rather than saying it simply disappears.
- 💡Use the phrase 'amplitude decreases exponentially' for light damping and reserve 'no overshoot' for critical damping to keep descriptions precise.
- 💡Plot amplitude against driving frequency and mark the resonant peak clearly, labelling the natural frequency on the frequency axis.
- 💡Repeat each run with different damping so you can describe how the peak becomes lower and broader as damping increases.
- 💡Note the practical precautions you took, such as waiting for steady state and keeping the driving amplitude constant, so you can justify your method.
- 💡State clearly that resonance occurs when driving frequency equals natural frequency, and link this to maximum amplitude.
- 💡When describing the effect of damping on the resonant peak, mention both height and width to show full understanding.
- 💡Use a labelled amplitude–frequency graph to support your explanation, marking the natural frequency and the peak.
- 💡State the axes and units before interpreting any feature of the graph.
- 💡Compare peak heights to rank damping levels, then compare widths to confirm the ranking.
- 💡When asked to explain a curve, link low damping to a large resonant amplitude and a narrow frequency band.
- 💡Check whether the question asks about amplitude, energy or phase before choosing an answer.
- 💡Name the driver, the driven system and the natural frequency in each example.
- 💡Use the phrase 'driving frequency equals the natural frequency' when defining resonance.
- 💡Mention damping when explaining why real resonant amplitudes are finite.
Common Mistakes
- Thinking a forced oscillator always vibrates at its natural frequency: it vibrates at the driving frequency.
- Believing resonance gives infinite amplitude in every real system: damping limits the maximum amplitude.
- Confusing free oscillation with zero damping: a free oscillation can still be damped and decay in amplitude.
- Assuming damping increases the resonant amplitude: damping reduces it and widens the response curve.
- Treating the label (b) as a fact to be memorised and recited in an examination answer, rather than as a heading that groups the sub-parts (i) and (ii). Correction: use (b) only to organise your revision and answer the actual sub-part statements.
- Revising only the theory of damping and skipping the practical observation required by sub-part (ii). Correction: plan both the conceptual work on the effects of damping and the experimental work on forced and damped oscillations.
- Assuming that because (b) has no wording of its own it cannot be assessed. Correction: the sub-parts beneath it are examinable, so prepare them fully.
- Reading the sub-parts out of order and missing how the effects of damping connect to the observation of forced and damped oscillations. Correction: study (i) and (ii) as a linked pair.
- Believing that damping changes the period of a lightly damped oscillator appreciably. Correction: for light damping the period is almost unchanged; the main observable effect is the decaying amplitude.
- Confusing heavy damping with critical damping. Correction: heavy damping returns the system to equilibrium slowly, while critical damping returns it in the shortest time without overshoot.
- Thinking that damping adds energy to the system. Correction: damping removes energy, typically transferring it to thermal stores, which is why the amplitude falls.
- Assuming a damped system stops oscillating immediately. Correction: light damping allows many oscillations with gradually decreasing amplitude.
- Recording only the driving frequency and forgetting to measure the amplitude of the steady-state oscillation. Correction: measure both, since the amplitude–frequency relationship is the key observation.
- Taking readings before the system has settled into steady-state oscillation. Correction: wait for the transient behaviour to die away before recording each amplitude.
- Assuming the observed amplitude is the same as the driving amplitude. Correction: the observed amplitude is the response of the oscillating system, which depends on the driving frequency.
- Ignoring damping when comparing runs. Correction: deliberately vary the damping so that its effect on the resonant peak can be observed and described.
- Defining resonance as any large oscillation. Correction: resonance specifically requires the driving frequency to equal the natural frequency.
- Confusing natural frequency with driving frequency. Correction: the natural frequency belongs to the system itself, while the driving frequency is set by the external periodic force.
- Thinking that damping increases the height of the resonant peak. Correction: greater damping lowers and broadens the peak; lighter damping gives a taller, narrower peak.
- Assuming resonance always causes destructive effects. Correction: resonance can be useful, for example in musical instruments, as well as hazardous, for example in structures.
- Confusing the natural frequency with the driving frequency at which amplitude is largest; the peak is at the driving frequency nearest the natural frequency, not at an arbitrary point.
- Thinking that heavier damping increases the resonant amplitude; heavier damping always reduces the peak amplitude and broadens the curve.
- Assuming all curves peak at exactly the same driving frequency; increased damping shifts the peak slightly below the undamped natural frequency.
- Reading the vertical axis as acceleration or energy rather than steady-state amplitude.
- Describing resonance as any large vibration rather than a response to a driving frequency matching the natural frequency.
- Forgetting the driving force and treating a free oscillation as a forced oscillation.
- Ignoring damping and claiming the amplitude grows without limit in a real system.
- Citing microwave heating of water as resonance: the error is thinking microwaves match a natural frequency; the correction is that microwaves heat via dielectric heating, not resonance.