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I have read about the term natural frequency in quite a lot of places. But I haven't found an explanation as to what is vibrating. It was pretty awkward when I couldn't clearly answer my little sister when she asked me to explain natural frequency and resonance. While studying dynamic analysis, I have actually determined this natural frequency for a variety of systems. But when I really thought of it, I just haven't been to clearly define the term natural frequency. And this question further leads me on to the phenomenon of Resonance. I have heard that failure by resonance is the reason for soldiers not marching on bridges, and this phenomenon is the exact reason why beats occur. So the objective of this question is to explain fundamental frequency in terms of what vibrates and what causes the vibrations and to explain the phenomenon of resonance based on the above explanation.

EDIT: All the answers are helpful. But the objective, as I have clearly mentioned, is to make me understand. So I would appreciate it if you could give the complete picture, which I haven't got from any of the answers as of yet!

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Since you want to answer a small child, I'd just start with a weight on a spring, preferably with a physical demo at hand. Show how it bounces at a specific rate regardless of how you initially stretch it out. Then maybe show a different resonant rate when you change the weight, or length of spring. That takes care of the "natural resonance frequency" part.

Then, maybe a bit more tricky: gently tap the weight (vertically) at the resonance rate and show the amplitude growing. Then tap at some other rate and observe the amplitude collapsing or going pseudorandom.

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  • $\begingroup$ @don_Gunner94 I've found the swing is a better example for a child to relate to. $\endgroup$ – docscience Jan 29 '15 at 16:01
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The natural frequency (or frequencies) isn't about what started the vibration, it is a property of the object: it "prefers" to vibrates that way, and getting to vibrate another way is harder.

Take an object, say a bell. Hit with a hammer.

When you first hit it there are vibration of many different frequencies started in the material. Most of those are no where near the natural frequencies of the object and so will die away quickly. Those that are near the natural frequencies will last longer because vibration loses energy more slowing in those modes, so the natural frequency will persist longer than other modes. High quality bells and gong can ring at their natural tones for a very long time indeed.

Resonance concerns what happens when you don't just hit the object once, but continue to shake it steadily. Energy can build up in the vibration of the object and it will do so most effectively at driving frequencies near the natural (or resonant) frequency of the object.

Now, I've short changed you a little bit because I haven't talked about overtones, but that for another question.

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  • $\begingroup$ This is good stuff. But what influences this property? Also why is it said that each degree of freedom has its own natural frequency. Could you explain that? $\endgroup$ – don_Gunner94 Jan 29 '15 at 15:34
  • $\begingroup$ Size, shape, and material control the values. Alas, the relationships are not simple except in simple geometries (a right angle box us the easy one). How comfortable are you with sound as a wave and the mathematics of waves? $\endgroup$ – dmckee Jan 29 '15 at 15:43
  • $\begingroup$ The onset of resonance depends not only on the rate of energy pouring into a system that has tendency to vibrate, but also the rate at which energy is lost by the system. If the two rates are equal you have a dynamic equilibrium - a stable limit cycle. If the energy going in exceeds the energy lost something eventually gives - as what happened to the Tacoma Narrows Bridge. $\endgroup$ – docscience Jan 29 '15 at 15:47
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    $\begingroup$ @don_Gunner94 regarding 'modes' a good example that can be used to explain to your sister is the playground swing - a type of pendulum. The normal mode is where energy is pumped into the swing in a forward or backward motion either by the parent pushing at just the right moment or the child swing their legs. But another mode can also be excited by twisting the swing - a torsional mode. In the normal mode gravity and length of the pendulum determine the natural frequency. In the torsional mode the tension of the supporting chains or rope and the mass of the child (cont) $\endgroup$ – docscience Jan 29 '15 at 15:55
  • $\begingroup$ @don_Gunner94 ... (actually the moment of inertia) dtermine the natural frequency. In both cases you have a harmonic oscillator, and as long as you feed energy at the rate which it is lost, and which can be received by the respective mode, you have resonance. $\endgroup$ – docscience Jan 29 '15 at 15:56

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