Natural frequency of oscillation and resonance

Thanks to the development of vibratory motion, a series of intrinsic phenomena are developed among which we have the sound, and this at the same time when it propagates through a material or elastic medium such as air, comes into contact with any body or object which activates another phenomenon such as acoustic resonance.

Therefore, in this opportunity we will analyze the phenomenon of resonance and the natural frequency of oscillation, where we will identify resonance from a generalized view and then relate it to the phenomenon of sound, whose waves as we have expressed are longitudinal sound waves of pressure.

The sound is originated by the vibratory motion of those particles components of certain bodies or objects, and this, either of natural or artificial origin, and of course, these particles when vibrating develop an oscillatory motion, and the latter consists of a back and forth movement, ie from one side to the other, where we have as reference a stable equilibrium position.

It is important to note that when a certain particle, body or object carries out a back-and-forth motion from end to end, that is, passing twice through the stable equilibrium position, we are talking about a complete cycle or oscillation, therefore, the number of complete cycles or oscillations in relation to a given unit of time is known as frequency, and the distance which is traveled from one end to the stable equilibrium point is known as amplitude, this can be seen in Figure 1 below.


Figure 1. Simple oscillatory motion

To analyze the phenomenon of resonance in general terms it is important to relate to the oscillatory motion and the natural frequency of oscillation, and this phenomenon (resonance) takes place when a given system oscillates when a force is applied to it periodically, and in addition, these oscillations approach or approach the natural frequency of oscillation of the perturbed system.


It is no secret that the great evolution of the technological field, together with science, has allowed us to broaden our range of observation of different phenomena imperceptible to any of our senses.

In this opportunity we will relate to the phenomenon of resonance and the natural frequency of oscillation of the component particles of certain bodies or objects, this phenomenon sometimes we can perceive it and sometimes it is not possible to do so, however, from that scientific-experimental view this range of observation increases significantly.

In relation to the natural oscillation frequency, it is necessary to point out that when we apply an external force to a given system, we disturb its stable equilibrium, and therefore, the system begins to oscillate, and it will continue to do so despite the removal of the external force.

In relation to the above, we can say that these oscillations of the analyzed system will be performed in a certain time and at a certain frequency, therefore, my dear friends, the frequency described above is known as the natural frequency of oscillation.

It is important to emphasize that every system has one or several natural oscillation frequencies, and the development of the resonance phenomenon in any system will depend on this, therefore, we can describe that the resonance phenomenon originates when a certain body or mechanical system is able to vibrate by the action of an external force, and also periodically, and thus, it approaches its natural oscillation frequency, and in this way the oscillations are becoming larger and larger, thus increasing the energy.

Next you will be able to observe a mechanical system such as the one constituted by a mass-spring, which will be in its stable equilibrium position as we can see in the following figure 2.


Figure 2. Traditional oscillatory motion mass-spring system at rest

We could see how in the previous figure 2, the previous system to be subjected to the action of an external force is managed to disturb the system, and thus the mass (m) located at the free end of the spring or spring begins to oscillate, and this despite we stop applying the external force, and also its movement will not stop immediately but gradually due to the rose with the air.

The value of the natural frequency of oscillation of such a system will depend on the elastic capacity of the spring and, of course, on the value of the mass (m) attached to it, highlighting the fact that if there were no friction or damping around the system, it would oscillate indefinitely.

Until another installment, my dear readers.

Note: The images are my own and were created using Power Point and the animated gifs were created using the PhotoScape application.

Recommended Bibliographic References

[1]Physics of sound

[2]Specular and diffuse sound reflection. Author: @rbalzan79.

[3]Sound absorption. Author: @rbalzan79.

[4]Sound transmission. Author: @rbalzan79.

[5]Sound diffraction. Author: @rbalzan79.

[6]Sound refraction. Author: @rbalzan79.

[7]Acoustic or sound spectrum. Author: @rbalzan79.

[8]The human ear and sound. Author: @rbalzan79.


[10]Educating ourselves with infrasound, Some sources of generation. Author:@rbalzan79.

[11]Educating ourselves with ultrasound. Author:@rbalzan79.

[12]Educating ourselves with ultrasound / Application in navigation. Author:@rbalzan79.

[13]Ultrasound technology applied in medicine. Author:@rbalzan79.