13.10 Resonance Graphs

• A graph of driving frequency f against amplitude A of oscillations is called a resonance curve. It has the following key features:
  • When f < f₀, the amplitude of oscillations increases
  • At the peak where f = f₀, the amplitude is at its maximum. This is resonance
  • When f > f₀, the amplitude of oscillations starts to decrease

The maximum amplitude of the oscillations occurs when the driving frequency is equal to the natural frequency of the oscillator

• Damping reduces the amplitude of resonance vibrations
• The height and shape of the resonance curve will therefore change slightly depending on the degree of damping
  • Note: the natural frequency f₀ of the oscillator will remain the same

• As the degree of damping is increased, the resonance graph is altered in the following ways:
  • The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
  • The resonance peak broadens
  • The resonance peak moves slightly to the left of the natural frequency when heavily damped

• Therefore, damping reduced the sharpness of resonance and reduces the amplitude at resonant frequency

As damping is increased, resonance peak lowers, the curve broadens and moves slightly to the left