Why does pushing a swing at just the right rhythm make it swing higher and higher?
Free and forced vibrations, damping, resonance and the effect of damping on the sharpness of the resonance peak.
A focused answer to AQA A-Level Physics 3.6.1.4, covering free and forced vibrations, the types of damping, resonance at the natural frequency, and how damping reduces and broadens the resonance peak.
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What this dot point is asking
AQA specification point 3.6.1.4 wants you to distinguish free and forced vibrations, describe light, heavy and critical damping, explain resonance in terms of a driving frequency matching the natural frequency, and describe how increasing damping lowers and broadens the resonance peak and shifts the maximum to a slightly lower frequency.
Free and forced vibrations
The natural frequency is fixed by the properties of the system, for example for a mass on a spring. When a driver is applied, the steady-state oscillation settles to the driving frequency, but the amplitude depends strongly on how close that frequency is to the natural frequency.
Damping
Damping is the removal of energy from an oscillating system by resistive forces (such as air resistance or friction), reducing the amplitude over time. The energy is dissipated as heat.
- Light damping: the amplitude decreases gradually over many oscillations, following an exponential decay envelope while the period stays almost unchanged.
- Heavy (over) damping: the system returns to equilibrium slowly without oscillating at all.
- Critical damping: the system returns to equilibrium in the shortest possible time without overshooting, as in car suspension and door closers.
Resonance
Increasing the damping reduces the peak amplitude, broadens the resonance curve, and moves the maximum to a slightly lower frequency than the undamped natural frequency. Engineers exploit damping to prevent destructive resonance in bridges, buildings and machinery, and to design suspension systems and shock absorbers.
Try this
Q1. State the condition for resonance. [1 mark]
- Cue. The driving frequency equals the natural frequency of the system.
Q2. Describe the effect of increasing damping on the resonance curve. [2 marks]
- Cue. The peak amplitude falls, the curve broadens, and the maximum shifts to a slightly lower frequency.
Q3. Give one example of a system designed to be critically damped. [1 mark]
- Cue. A car suspension system (or a self-closing door mechanism).
Exam-style practice questions
Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AQA 20194 marksExplain what is meant by resonance, and describe how the amplitude of a lightly damped system varies as the driving frequency is increased from below to above the natural frequency.Show worked answer →
Resonance occurs when the driving frequency equals the natural frequency of the system. Energy is then transferred from the driver to the oscillator most efficiently, so the amplitude reaches a maximum.
As the driving frequency increases from a low value, the amplitude is small at first, rises to a sharp maximum at the natural frequency, and then falls again as the frequency increases beyond it. For light damping this peak is tall and narrow.
Markers reward defining resonance as the frequency match, the efficient energy transfer, and the rise-then-fall shape with a sharp peak at the natural frequency.
AQA 20214 marksDescribe the effect of increasing the degree of damping on the resonance curve of a forced oscillator, and give one practical example where damping is deliberately used.Show worked answer →
Increasing the damping lowers the peak amplitude of the resonance curve and broadens it, so the response is spread over a wider range of frequencies. The frequency at which the maximum amplitude occurs also shifts to a value slightly below the undamped natural frequency.
A practical example is a car suspension system, which is critically (or close to critically) damped so the car returns smoothly to equilibrium after a bump without oscillating, or the deliberate damping of tall buildings and bridges to prevent destructive resonance.
Markers reward lower peak, broader curve, slight downward shift of the maximum, and a valid practical example.
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Sources & how we know this
- AQA A-level Physics (7408) specification — AQA (2017)