9702 · 17.3
Damped and forced oscillations, resonance flashcards
Revision flashcards for Cambridge 9702 Damped and forced oscillations, resonance (syllabus 17.3). Flip, recall, then mark a real past-paper question.
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What is the fundamental definition of damping in an oscillating system?
Damping is the process where energy is gradually lost from an oscillating system, causing the amplitude of its oscillations to decrease over time.
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How does critical damping differ from overdamping in terms of returning to equilibrium?
Critical damping allows a system to return to its equilibrium position in the fastest possible time without any oscillation. Overdamping also prevents oscillation but takes a longer time to return to equilibrium.
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What specific condition must be met for resonance to occur in a forced oscillation?
Resonance occurs when the driving frequency of the external periodic force precisely matches the natural frequency of the oscillating system.
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What is the primary consequence of resonance on the amplitude of an oscillating system?
Resonance leads to a significant and often dramatic increase in the amplitude of oscillations, due to highly efficient energy transfer from the driving force.
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How does increased damping affect the peak amplitude and sharpness of a resonance curve?
Increased damping reduces the maximum amplitude achieved at resonance and broadens the resonance curve, making the peak less sharp.
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What are free oscillations?
Free oscillations occur when a system oscillates at its natural frequency without any external driving force acting upon it.
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What are forced oscillations?
Forced oscillations happen when an external periodic force continually drives a system to oscillate at the driving frequency of that external force.
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Provide an example of a useful application of resonance.
Useful applications include tuning radio circuits to receive specific stations or the production of sound in musical instruments like a guitar string or flute.
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Provide an example of an undesirable effect of resonance.
Undesirable effects can include structural damage to bridges from strong winds or excessive vibrations in machinery operating near its natural frequency.
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How does underdamping (light damping) appear graphically on an amplitude-time graph?
Underdamping results in oscillations with an amplitude that progressively decreases, often showing an exponential decay, before the system eventually comes to rest.
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What is the 'natural frequency' of an oscillating system?
The natural frequency is the specific frequency at which a system will oscillate if it is displaced from equilibrium and then allowed to oscillate freely, without any external driving forces or damping.
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What is the relationship between power supplied and power dissipated in a forced oscillation at constant amplitude?
For a forced oscillation to maintain a constant amplitude, the average power supplied by the driving force must be equal to the average power dissipated by the damping forces.