# Resonance

In sound applications, a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics. Some of the implications of resonant frequencies are:

 1. It is easy to get an object to vibrate at its resonant frequencies, hard to get it to vibrate at other frequencies. Example 2. A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation. Example 3. Most vibrating objects have multiple resonant frequencies. Example
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# Ease of Excitation at Resonance

It is easy to get an object to vibrate at its resonant frequencies, hard at other frequencies. A child's playground swing is an example of a pendulum, a resonant system with only one resonant frequency. With a tiny push on the swing each time it comes back to you, you can continue to build up the amplitude of swing. If you try to force it to swing a twice that frequency, you will find it very difficult, and might even lose teeth in the process!

 Swinging a child in a playground swing is an easy job because you are helped by its natural frequency. But can you swing it at some other frequency?
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# Picking out resonant frequencies

A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

 If you just whack a mass on a spring with a stick, the initial motion may be complex, but the main response will be to bob up and down at its natural frequency. The blow with the stick is a complex excitation with many frequency components (as could be shown by Fourier analysis), but the spring picks out its natural frequency and responds to that.
 Square wave example
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