Resonance
Oscillations - OCR A-Level Physics
Key Definition
Resonance
The condition where a system is driven at a frequency equal to (or very close to) its natural frequency, causing the amplitude of oscillation to increase dramatically.
The condition where a system is driven at a frequency equal to (or very close to) its natural frequency, causing the amplitude of oscillation to increase dramatically.
- At resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energyThe capacity to do work. Measured in joules (J). transfer., the driving frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). equals the natural frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).The frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). at which a system oscillates freely when displaced from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. and released, with no external driving force.: $f_{driver}$ = f_0.
- At resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energyThe capacity to do work. Measured in joules (J). transfer., the system absorbs energyThe capacity to do work. Measured in joules (J). most efficiently from the driver.
- At resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energy transfer., the velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. of the oscillator is in phaseTwo oscillations that are exactly synchronised — zero phase difference (or a whole number of cycles apart). with the driving force (phase $difference = 0 between$ force and velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.).
- The displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). lags the driving force $by \pi/2$ ($90\degree$) at resonance.
- Damping reduces the resonance peak: the maximum amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). is lower, the peak is broader (less sharp), and the peak frequency shifts slightly below f_0.
- With heavy dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance., the resonance peak almost disappears.
- Examples of resonance: Tacoma Narrows bridge collapse, tuning a radio, microwave ovens (water molecule resonant frequency), MRI scanners, pushing a swing.
- Examples of useful dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance.: car shock absorbers (critical dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance.), earthquake-resistant buildings, noise-cancelling headphones.
Common Mistake
MEDIUM
Wrong: Saying that damping changes the natural frequencyThe frequency at which a system oscillates freely when displaced from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocity. and released, with no external driving force. of the system.
Right: Damping does NOT change the natural frequencyThe frequency at which a system oscillates freely when displaced from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocity. and released, with no external driving force.. It reduces the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). at resonance and slightly shifts the peak of the resonance curve to a lower frequency, but the natural frequencyThe frequency at which a system oscillates freely when displaced from equilibrium and released, with no external driving force. itself (determined by mass and stiffness) is unchanged.
Right: Damping does NOT change the natural frequencyThe frequency at which a system oscillates freely when displaced from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocity. and released, with no external driving force.. It reduces the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). at resonance and slightly shifts the peak of the resonance curve to a lower frequency, but the natural frequencyThe frequency at which a system oscillates freely when displaced from equilibrium and released, with no external driving force. itself (determined by mass and stiffness) is unchanged.