Forced Oscillations and Resonance
Forced Oscillations and Resonance
- A free oscillator moves at its own natural frequency after one disturbance. A forced oscillator receives a repeated external force.
Natural frequency and the driving force
Definition
1 markWhat is meant by natural frequency?
Model answer: The frequency at which a system oscillates freely after it is moved away from equilibrium and released.
Definition
1 markWhat is meant by a forced oscillation?
Model answer: An oscillation maintained by a repeated external driving force.
- During a forced oscillation, the system follows the frequency of the driver.
- The response depends on how close the driving frequency is to the natural frequency.
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The two-mark resonance definition
Definition
2 marksWhat is meant by resonance?
Model answer: The condition in which a forced oscillator has maximum amplitude because the driving frequency equals its natural frequency.
Maximum amplitude and equality of the two frequencies are the two marks (9702/41/M/J/24 Q4(a)).
- A correctly timed force acts in the direction of motion. It adds energy on each cycle.
- At resonance, energy is transferred from the driver at the greatest rate, so the amplitude becomes largest.
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- The exam sketch needs one clear maximum at a non-zero frequency. Place the maximum at the natural frequency.
- More damping makes the resonance peak lower and broader. Less damping gives a taller, narrower peak.
Resonance is not simply “a large vibration”. State both conditions: maximum amplitude, and driving frequency equal to natural frequency.
When resonance helps and when it is dangerous
Child on a swing
Oscillator: swing and child. Driver: repeated pushes.
The amplitude grows.
Radio tuning
Oscillator: electrical circuit. Driver: incoming signal.
One frequency gives a large response.
Bridge or building
Oscillator: structure. Driver: repeated steps, wind or ground motion.
Large motion may cause damage.
- Dangerous resonance is reduced by adding damping. The damping transfers energy away and limits the amplitude.
- Engineers may also change the natural frequency so that it no longer matches the expected driving frequency.