Damping, Natural Frequency and Resonance

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Damping, Natural Frequency and Resonance

In practice, the amplitude of vibrations becomes progressively smaller as energy is lost due to friction between the oscillating body and the particles in the air.

If energy is being removed from the system, the amplitude of the oscillations must become smaller and smaller, we say that the oscillations are being damped.

  • The amplitude of oscillations decrease with time.
  • The higher the damping, the faster the oscillations will reduce in size.

Critical damping is the damping required to make the oscillations stop in the quickest possible time without going past the equilibrium position.

Damping of free vibrations:

Damping, Natural Frequency and Resonance

Damping of forced Vibrations:

Damping, Natural Frequency and Resonance

Note: That the lines in the graph never touch or cross. Also, note that if the system becomes heavily damped, the peak of the light blue line will move slightly to the left - to a slightly lower value of natural frequency.

It is sometimes useful to damp vibrations. For example, car suspensions are damped to stop them bouncing for a long time.

However, if the car suspensions are over damped then the car may jolt uncomfortably every time the car goes over a bump in the road. Over damping also means that there is a long delay before the suspension can react to any more bumps.


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Hit anything and it will vibrate. The amazing thing is that every time you hit it, it will vibrate with exactly the same frequency, no matter how hard you hit it.

The frequency of un-damped oscillations in a system, which has been allowed to oscillate on its own, is called the natural frequency, f0.

In order to keep it vibrating after you've hit it, you need to keep re-hitting it periodically to make up for the energy being lost. We say that you need to apply a periodic force to it. (Although some people would just say that you are being unnecessarily violent.)

The frequency with which the periodic force is applied is called the forced frequency. If the forced frequency equals the natural frequency of a system (or a whole number multiple of it) then the amplitude of the oscillations will grow and grow. This effect is known as resonance.

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Don't try this at home!

Interesting point: During resonance vibrations can build up to dangerous levels...

  • Washing machines and buses will often vibrate violently when the engine oscillates at their natural frequency.
  • It is resonance that smashes a glass when an opera singer hits the note that is the natural frequency of the glass.
  • Resonance is also why soldiers break their march to cross a bridge - otherwise resonance may cause the bridge to vibrate so violently that it collapses.

Resonance has many uses, for instance:

  • Musical instruments - for example, wind and string instruments.
  • Circuits can use electrical resonance - for example, for selecting communication channels.


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