3.6.1.4
The resonance curve shows amplitude peaking at the natural frequency
Forced Vibrations & Resonance — AQA A-Level Physics
- A 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. curve plots amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (y-axis) against driving frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). (x-axis).
- When f < f_0: amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). increases as f approaches f_0.
- At f = f_0: amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). is at its maximum. This is 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..
- When f > f_0: amplitude decreases as f moves away from f_0.
- The peak is centred on f_0.
Effects of dampingThe reduction in amplitude (and energyThe capacity to do work. Measured in joules (J).) of an oscillation over time due to resistive forces such as friction or air resistance. on the resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energy transfer. curve
- More dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance. lowers the peak amplitude.
- More dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance. broadens the resonance peak (the response becomes less sharp).
- More damping shifts the peak slightly to the left of f_0.
- 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_0 itself does not change with damping.
- With no damping, the amplitude at resonance would theoretically be infinite.
Examiner Tips and Tricks
- When sketching resonance curves with different damping levels, the peaks should all be centred at roughly the same frequency.
- The heavily damped curve should be much wider and lower, with its peak slightly left of f_0.