How do damping and a driving force change an oscillation, and why does resonance produce such large amplitudes?
Vibrations: free and forced oscillations, light, heavy and critical damping, the resonance condition, and the effect of damping on the resonance curve.
A focused answer to the Eduqas A-Level Physics Component 1 content on damping and resonance, covering free and forced oscillations, light, heavy and critical damping, the resonance condition when the driving frequency matches the natural frequency, and how damping affects the resonance curve.
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What this dot point is asking
Eduqas wants you to distinguish free from forced oscillations, describe light, heavy and critical damping, state the resonance condition, and explain how increasing the damping changes the resonance curve.
The answer
Free and forced oscillations
Damping
The resonance condition
The effect of damping on resonance
Examples in context
Resonance is exploited in musical instruments, radio and television tuning (matching a circuit's natural frequency to a station), and magnetic resonance imaging. It can also be destructive: soldiers break step on bridges, and the wind drove the Tacoma Narrows Bridge to catastrophic oscillation. Engineers add dampers (tuned mass dampers in skyscrapers, shock absorbers in cars) to control unwanted resonance, and aim for near-critical damping so vehicles and instruments settle quickly.
Try this
Q1. State the difference between a free and a forced oscillation. [2 marks]
- Cue. A free oscillation is at the natural frequency with no driving force; a forced oscillation is driven and occurs at the driving frequency.
Q2. State the condition for resonance to occur. [1 mark]
- Cue. The driving frequency equals (or is very close to) the natural frequency.
Q3. State how increasing the damping changes the resonance peak. [2 marks]
- Cue. It lowers and broadens the peak (and shifts it slightly to a lower frequency).
Exam-style practice questions
Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Eduqas 20204 marksExplain the difference between free and forced oscillations, and state the condition under which resonance occurs.Show worked answer →
A free oscillation occurs when a system is displaced and released, then oscillates at its own natural frequency with no external periodic force and (ideally) no energy loss.
A forced oscillation occurs when a system is driven by an external periodic force; it then oscillates at the driving frequency, not necessarily its natural frequency.
Resonance occurs when the driving frequency equals (or is very close to) the natural frequency of the system. At resonance energy is transferred most efficiently from the driver to the system and the amplitude reaches a maximum.
Markers reward the definition of a free oscillation (natural frequency, no driving), a forced oscillation (driven at the driving frequency), and the resonance condition (driving frequency equals natural frequency).
Eduqas 20214 marksA mass-spring system is driven at a range of frequencies. Sketch how the amplitude of oscillation varies with driving frequency, and describe how the curve changes if the damping is increased.Show worked answer →
The amplitude-against-driving-frequency curve rises to a sharp peak at the natural (resonant) frequency, then falls again at higher frequencies.
Increasing the damping lowers the height of the peak (a smaller maximum amplitude), broadens it, and shifts the peak slightly to a lower frequency than the undamped natural frequency.
Markers reward a peak at the natural frequency, and stating that more damping lowers and broadens the peak (and shifts it slightly lower).
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Sources & how we know this
- Eduqas GCE AS/A Level Physics specification (A720QS) — WJEC Eduqas (2015)