8.5.2 Resonance Curve

Consider an oscillatory system with natural frequency f0. Let’s couple this system to a driver. We can set the driver to vibrate with a fixed amplitude A0 at different driving frequency f.

If we plot on a graph how the amplitude of the forced oscillation A varies with the driver’s frequency f, we obtain the so-called resonance curve.

Notice that

  • Amplitude A peaks at \displaystyle f={{f}_{0}}.

When the driver is driving at the natural frequency of the oscillator, it’s like a match made in heaven. The energy transfer from the driver to the oscillator is at its most efficient. In fact, the oscillator is able to accumulate the energy transferred and reaches a maximum amplitude that is many times larger than the amplitude of the driver.

  • As f approaches 0, A approaches A0.

When a slow driver meets a quick oscillator, the oscillator is so “nimble” it tracks the motion of the driver exactly. So the oscillator has the same amplitude of oscillation as the driver.

  • As f approaches infinity, A approaches zero.

When a quick driver meets a slow oscillator, the oscillator is so “retarded” it simply cannot respond in time. The driving forces changes too rapidly for the oscillator and its amplitude is stuck at zero.

Video Explanation

Resonance Curve

Concept Test

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