Natural frequency

[Jenny_95]

I was studying free undamped vibration, and i have this question 

What is the difference between the Natura frequency of a system and the frequency of any signal (f=1/period = natural frequency /2pi)

[quiet]

Some systems have the following property. When you deliver energy to the system, the system initiates an oscillation that has a characteristic frequency. This frequency does not depend on what you do to provide the energy. It only depends on the constitution of the system.

This is how they behave, for example, a mass / spring system, a parallel LC circuit, a piano string with the structure that holds it tense, a pendulum.

Mass / spring [math] \rightarrow [/math] You can gently take the dough and make a movement that stretches the spring, you can shake the table that holds the system, you can aim a fan to cause some movement, whatever you want. You will always observe the same frequency of oscillation.

Parallel LC circuit [math] \rightarrow [/math] You can take a battery and make a spark at the terminals of the circuit, you can take a magnet and move it close to the coil. The oscillation frequency is always the same.

Piano string [math] \rightarrow [/math] You can press the key that moves the hammer and hits the string, you can lift the top of the piano and hook the string with your fingernail, you can rub the string. The frequency, that is, the note, is always the same.

Pendulum [math] \rightarrow [/math] You can take the weight with your hand and move it, if the weight is ferrous you can zoom in on a magnet and cause movement, you can aim a fan, whatever you want. The pendulum will always oscillate with the same frequency. That's why pendulum clocks have been pretty good.

You have asked about a signal. Example, emitting radio waves. It is true that in the emission you are delivering energy to the space that surrounds you. And in this case, space is not responsible for always establishing waves of the same frequency, regardless of what you do. It's the other way around. The frequency of the broadcast depends on what you do. If your mode of emitting is to shake a magnet, the rhythm of your hand establishes the frequency, not the space through which the emission propagates. The same if you shake an electric charge. And if you use a transmitter device of the usual type, the frequency depends on how you control the transmitter, it does not depend on the surrounding space.

Edited December 9, 2018 by quiet