OCR · A-Level · Physics

    Course version: H556 · Version from Sept 2015

    Damping: (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.

    Checked against the OCR H556 specification (opens in a new tab) on .

    • Point 5 of 5
    • 3 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    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.

    What earns the marks

    • 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.

    Common mistakes and how to put them right

    • 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.

      Put it right: Microwaves heat via dielectric heating, not resonance.

    Exam tips

    • 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.

    Try the lesson

    The start of the Damping: (e) practical examples of forced oscillations and resonance. lesson, made from checked teaching notes for this specification point.

    Listen

    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. A strong answer earns marks for these points. 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. A common slip: Citing microwave heating of water as resonance: the error is thinking microwaves match a natural frequency. Instead, microwaves heat via dielectric heating, not resonance. Exam tip: Name the driver, the driven system and the natural frequency in each example.

    See it

    A flowchart running from top to bottom. The first box reads 'Periodic driving force applied' and points to a second box, 'Forced oscillation at driving frequency'. This leads to a decision box, 'Driving frequency equals natural frequency?'. The 'Yes' branch goes to 'Resonance: large-amplitude response'; the 'No' branch goes to 'Steady-state amplitude depends on driving frequency and damping'. From the resonance box, one arrow leads to 'Damping removes energy', which then splits into two boxes: 'Resonant amplitude limited, not indefinite' and 'Resonant frequency slightly reduced'. A second arrow from the resonance box leads to 'Examples: swing, Barton's pendulums, washing machine, structures'.
    It shows how a periodic driving force produces a forced oscillation, how matching the driving frequency to the natural frequency gives resonance, and how damping limits the resonant amplitude and slightly reduces the resonant frequency.

    Key words

    Say what each word means before you turn the card.

    Forced oscillation

    Try answering aloud or in your head before turning the card.

    Resonance

    Try answering aloud or in your head before turning the card.

    Damping

    Try answering aloud or in your head before turning the card.

    See every definition
    Forced oscillation
    A periodic driving force is applied to a system, which then oscillates at the driving frequency.
    Resonance
    The large-amplitude response when the driving frequency is equal to the system's natural frequency.
    Damping
    Removes energy from the system, preventing the resonant amplitude from increasing indefinitely and slightly reducing the resonant frequency.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A flowchart running from top to bottom. The first box reads 'Periodic driving force applied' and points to a second box, 'Forced oscillation at driving frequency'. This leads to a decision box, 'Driving frequency equals natural frequency?'. The 'Yes' branch goes to 'Resonance: large-amplitude response'; the 'No' branch goes to 'Steady-state amplitude depends on driving frequency and damping'. From the resonance box, one arrow leads to 'Damping removes energy', which then splits into two boxes: 'Resonant amplitude limited, not indefinite' and 'Resonant frequency slightly reduced'. A second arrow from the resonance box leads to 'Examples: swing, Barton's pendulums, washing machine, structures'.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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