AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Qualitative treatment of free and forced vibrations.
Full specification wording
Forced vibrations and resonance (A-level only): Qualitative treatment of free and forced vibrations.
A free vibration occurs when an object oscillates at its natural frequency after being displaced, with no periodic external force.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A free vibration occurs when an object oscillates at its natural frequency after being displaced, with no periodic external force. A forced vibration occurs when a periodic driving force makes the object oscillate at the driving frequency. At low driving frequencies the amplitude is small; as the driving frequency approaches the natural frequency the amplitude increases, reaching a maximum at resonance. The sharpness of the resonance curve depends on damping: heavier damping lowers and broadens the peak. You should describe these effects qualitatively, using examples such as a child on a swing pushed at the right moments, or a glass vibrating strongly when a sound wave matches its natural frequency.
What earns the marks
- Distinguishes free vibration, where the system oscillates at its natural frequency, from forced vibration, where a periodic driving force determines the frequency.
- States that the amplitude of a forced vibration depends on the difference between the driving frequency and the natural frequency.
- Describes resonance as the condition where driving frequency equals natural frequency and amplitude reaches a maximum.
- Explains that increased damping reduces the maximum amplitude and broadens the resonance peak.
- Applies the ideas to a named example, such as a swing pushed at its natural frequency or a building vibrating in an earthquake.
Common mistakes and how to put them right
Saying that a forced oscillator always vibrates at its natural frequency.
Put it right by stating that it vibrates at the driving frequency, with maximum amplitude when this equals the natural frequency.
Confusing resonance with any large vibration.
Put it right by linking resonance specifically to driving frequency matching natural frequency.
Ignoring damping when describing the resonance peak.
Put it right by explaining that damping lowers and broadens the peak.
Exam tips
- Use the terms driving frequency and natural frequency precisely in your answer.
- Sketch or describe the amplitude–frequency graph, marking the peak at the natural frequency.
- Link each statement to a familiar example so the qualitative explanation is clear.
Try the lesson
The start of the Forced vibrations and resonance (A-level only): Qualitative treatment of free and forced vibrations. lesson, made from checked teaching notes for this specification point.
Have a go first
A student holds the top of a simple pendulum and moves their hand from side to side at a constant frequency that is much lower than the pendulum's natural frequency. The pendulum swings at the frequency of the student's hand. Which term describes the vibration of the pendulum?
Listen
A free vibration occurs when an object oscillates at its natural frequency after being displaced, with no periodic external force. A forced vibration occurs when a periodic driving force makes the object oscillate at the driving frequency. At low driving frequencies the amplitude is small; as the driving frequency approaches the natural frequency the amplitude increases, reaching a maximum at resonance. The sharpness of the resonance curve depends on damping: heavier damping lowers and broadens the peak. You should describe these effects qualitatively, using examples such as a child on a swing pushed at the right moments, or a glass vibrating strongly when a sound wave matches its natural frequency. A strong answer earns marks for these points. Distinguishes free vibration, where the system oscillates at its natural frequency, from forced vibration, where a periodic driving force determines the frequency. States that the amplitude of a forced vibration depends on the difference between the driving frequency and the natural frequency. Describes resonance as the condition where driving frequency equals natural frequency and amplitude reaches a maximum. Explains that increased damping reduces the maximum amplitude and broadens the resonance peak. A common slip: Saying that a forced oscillator always vibrates at its natural frequency. Instead, stating that it vibrates at the driving frequency, with maximum amplitude when this equals the natural frequency. Exam tip: Use the terms driving frequency and natural frequency precisely in your answer.
Key words
Say what each word means before you turn the card.
Free vibration
Try answering aloud or in your head before turning the card.
Forced vibration
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Resonance
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Damping
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See every definition
- Free vibration
- Occurs when an object oscillates at its natural frequency after being displaced, with no periodic external force.
- Forced vibration
- Occurs when a periodic driving force makes the object oscillate at the driving frequency.
- Resonance
- The condition where driving frequency equals natural frequency and amplitude reaches a maximum.
- Damping
- Heavier damping lowers and broadens the resonance peak, reducing the maximum amplitude.
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