# Talk:Resonance

## Why is first picture in German in an English Article?

can we add some more detailed stuff about string resonance, tube resonance, impulse response, frequency response, stuff like that? maybe a swing set example, since that is something people understand easily. i don't know the details that well. also can we explain how the energy moves around in a resonant system? For instance... well... I don't even know a for instance. I don't understand it and I wish I did. Clearly a resonant system is passive, and doesn't create more energy than you put into it, but it somehow builds up that energy, and I obviously need this concept explained more clearly. I will do some research and help write it, but other people add stuff you know too. - Omegatron 14:16, May 21, 2004 (UTC)

Actually, should we make an article for Acoustic resonance and move some of this stuff over there? Along with the resonance bits from Acoustics. - Omegatron 15:36, Aug 6, 2004 (UTC)

## Increase in energy?

"is an increase in the oscillatory energy absorbed by a system"?

you mean an increase relative to other energy levels. resonance isnt an energy source... - Omegatron 18:11, Dec 9, 2004 (UTC)

One concept critical to understanding resonant absorption: in order to receive energy, the passive oscillator transmits. Resonant absorption might better be understood in the case of plane waves and diagrams involving diffraction patterns. If we have an incoming train of plane-waves, and if a small pointlike transmitter then sends out sphere-waves of the same frequency, and if the phase of the transmitted waves is adjusted in order to create a shadow in the region "downstream" from the transmitter... then we have resonant absorption occuring. By emitting a train of inverse waves, the "transmitter" has cancelled out some of the incoming waves; it has punched a hole in the plane waves, created a shadow, and a portion of wave-energy has gone missing. The missing energy ends up inside the point-like "transmitter." That's how resonant absorption occurs. If a passive oscillator such as an LC circuit is involved, then the oscillator is simultaneously "stealing energy" from the incoming wave while it also emits waves of its own. These concepts apply to resonant radio antennas, to resonant acoustic absorbers, and even to resonant atoms which "eat" light waves. The same explanation also applies to RLC circuits: a paired coil/capacitor acts as a passive oscillator which essentially sends out an inverse copy of the incoming signal. The two signals cancel. As a result, some energy has vanished from the original signal. The missing energy ends up inside the passive LC oscillator, and the oscillations grow larger until any further increase would "transmit" more energy than is being absorbed via the wave-cancellation process. (So, is this understandable? Too complicated?) --Wjbeaty 08:42, Apr 19, 2005 (UTC)
???
Can you draw or GIS some pictures? Passive systems clearly don't really transmit anything, so you're just using that idea as an example in some way, but I don't understand the example. - Omegatron 02:45, Apr 20, 2005 (UTC)
Ah, perhaps your first assumption is the problem. I meant what I said: passive systems definitely transmit, it's just that they cannot transmit anything more than they absorb. Also, as they are transmitting, they are simultaneously absorbing. For example, when a metal mirror reflects EM waves, the free electrons in the metal surface are oscillating coherently, and this is no different than the electric current in a radio transmitter antenna. In that sense, a mirror is an "energy source" since it radiates EM waves which it had absorbed. But obviously a mirror is not a *net* energy source. In many different systems the phenomenon of reflection is not a "bouncing" of waves, instead it's absorption combined with re-emission.
In the case of resonant absorption, the "absorber" behaves as a much better transmitter than it otherwise would, but this occurs only at one particular frequency. The "absorber" takes in wave-energy, then sends out an anti-wave which cancels out part of the incoming wave-energy, which allows the absorber to take in MORE wave energy, letting it transmit an even stronger anti-wave, etc. This is how all radio receiving antennas work. (Question: with antennas, why does a good transmitter make such a good receiver? Answer: It's because absorption is in fact based on the emission of an anti-wave. Whenever you design a good transmission antenna, you inadvertantly design a good receiving antenna, and you're amazed to find that the reception pattern is the same as the transmission pattern. ) --Wjbeaty 01:33, May 21, 2005 (UTC)
Hmm.. still confused. Reflection is not the same as transmission, and a transmitted wave cannot cancel out a received wave since they are going in opposite directions? - Omegatron 17:49, May 22, 2005 (UTC)

I reworded the definition slightly to remove the word "increase", which I admit was slightly ambiguous. --Heron 19:33, 22 May 2005 (UTC)

I must say, Wjbeaty has provided some food for thought - it will take some time to 'digest' what he has said above! W.r.t. Omegatron's question above, it is my understanding that a standing wave is due to the interaction of a transmitted and reflected wave where the nodes of the standing wave are due to the destructive interference of the two waves travelling in opposite directions.
Interestingly, it is always possible to obtain the solution for a system with reflection at the boundaries using the 'Method of Images' where each reflected wave is replaced with a transmitted wave from a source outside the boundaries of the system. Perhaps this is the key to Wjbeaty's post above.
One last comment - As mentioned above, a good absorber is necessarily a good transmitter. Consider the ideal Black body. Alfred Centauri 14:43, 21 August 2005 (UTC)

## Tacoma Narrows Bridge not destroyed by resonance

Here someone explains that the Tacoma Narrows Bridge is not a good example of resonance. Should the reference (or perhaps the whole paragraph) be removed?

The destruction of the Tacoma Narrows Bridge was indeed not caused by resonance, but the article is not claiming that it is. However, the bridge did suffer from resonance at other times, which is where the nickname "Galloping Gerdie" came from. At least, that is my understanding from reading Tacoma Narrows Bridge; perhaps a mechanical engineer can correct me. You may be right that we should not mention the Tacoma Narrows Bridge because it is a rather confusing example. However, the London Millennium bridge seems to be a proper example. -- Jitse Niesen 17:06, 7 Feb 2005 (UTC)
The Tacoma Narrows bridge was destroyed by resonance, but not in the way we might imagine. If we place an object in a flow of air, at certain wind speeds the downstream air turbulence takes the form of periodic counter-rotating vortices called a "Von Karman vortex street." (Imagine a flapping flag, then imagine a series of tornadoes shed by the flag and which continue far downstream.) At just the right wind speed the periodically varying wind direction and pressures caused by the wake-turbulence would have the same frequency as the bridge. Imagine a flapping flag which is connected to a pendulum: at certain wind speeds the flap-frequency would match the pendulum frequency, and the pendulum would go wild! If the pendulum frequency was very low, then only a very slow air motion would hit the right frequency. So, the bridge was resonantly pumped into motion by puffs of air, but these puffs of air were coming from downstream, and they were part of the natural (but invisible) turbulent wake that exists behind most objects exposed to wind. The same effect is often seen in power lines on days with almost no wind. The lines start swinging mysteriously because the very slow wind is creating some slow turbulence, and there is an "AC signal" in the turbulent air which matches the natural frequency of the swinging wires. The wires are pumped into large motion by their own air turbulence. --Wjbeaty 01:43, May 21, 2005 (UTC)
You are wrong Wjbeaty. I corrected the wikipedia article. I added the most important reference about that mistake that the Tacoma failed due to resonance. It failed due to fluttering. Robert Scanlan, father of bridge aerodynamics wrote an article on the subject... see main text:

Diego Torquemada 07:51, 5 April 2006 (UTC)

After browsing the linked document, it appears to me that, in EE language, the poles moved into the RHP. That is, with the wind as an energy source, the bridge became an oscillator. I assume that's what self-excited means in this context - there is an output at some frequency without a corresponding input at that frequency.
BTW, Diegotorquemada, beginning a sentence with "You are wrong..." is a great way to make friends around here. Wish I had thought of it. Alfred Centauri 03:44, 6 April 2006 (UTC)
sorry Alfred and Wjbeaty, next time I will measure better my words. What you say about the poles is right... when the poles of the bridge go to the right hand side, and have imaginary parts, fluttering is produced. There is another failure for bridges, that is when the pole in the RHS is purely real. In this case a failure called "divergence" is produced. It can be understood as a really flying bridge, because the deck just lifts on the presence of strong wind, making it literally fly, and since the tension in the hangers is lost, the bridge collapses by overturning. Diego Torquemada 07:42, 8 April 2006 (UTC)

## Resonant frequency or resonance frequency???

It appears that there is no such thing as a resonant frequency:

I recommend that the various 'resonant frequency' terms in the article be replaced with 'resonance frequency'. Alfred Centauri 02:41, 21 August 2005 (UTC)

I don't.
"The frequency at which resonance occurs is called the resonant frequency." -- A Dictionary of Physics. Ed. Alan Isaacs. Oxford University Press, 2000. Oxford Reference Online. Oxford University Press.
"At the resonant frequency, ..." -- "resonance" entry, Britannica Online, 2005.
"at the resonance frequency" -- "resonance" entry, Newnes Dictionary of Electronics on xreferplus, 2005.
"The resonant frequency is the frequency at which ..." -- "resonance" entry, The New Penguin Dictionary of Science, on xreferplus, 2005.
"is said to be .. the resonant frequency" -- "resonance", Penguin Dictionary of Physics, 1982.
"resonant frequency" (headword) -- Chambers Science and Technology Dictionary, 1988.
"resonant frequency" (headword) -- OED2, with citations from 1925, 1934, 1964.
I think FV Hunt is being unnecessarily pedantic. Most authorities write "resonant", but a few write "resonance". Who cares? It's only a shorthand term for a real concept - it doesn't alter the concept itself. It reminds me of the famous pedant C.P. Scott, who complained that television would never catch on because it was a hybrid of Greek and Latin roots. Hunt has a point, and perhaps "resonance frequency" is more accurate than "resonant frequency", and if you agree with him then you can write the former, but it's not a good enough reason to go changing what others have written. --Heron 11:46, 21 August 2005 (UTC)
I agree that no one will be confused by the use of 'resonant frequency' instead of 'resonance frequency'. On the other hand, it is my opinion that the author(s) of an encyclopedic article should and would care about 'getting it right'. After all, you do agree that "Hunt has a point". While I question your description of the changing of the word resonant to resonance as a 'rewrite' of the article, I do see your point. Accordingly, I have added the link above to the 'External Links' section of the article. Alfred Centauri 13:14, 21 August 2005 (UTC)
Thank you for accommodating my objection, Alfred. I accept that the word "rewrite" was an exaggeration and, to be honest, I suppose it won't hurt if you do decide to change the phrase throughout the article. My only concern is that you don't start telling people that they are "wrong" for using "resonant", as I think the distinction is too pedantic to matter. --Heron 14:59, 21 August 2005 (UTC)
Agreed. I hope I haven't developed a reputation on Wikipedia for nitpicking for any reason other than to spur intelligent conversation. Alfred Centauri 16:47, 21 August 2005 (UTC)

Here is how i look at it: A frequency doesn't resonate any more than a curve resonantes, a circuit can resonante hence resonance frequencies and resonance curves and resonant circuits. :>) TomPoindexter 20:40, 23 January 2007 (UTC)

I feel when technical terms are defined in an encyclopedia for nontechnical people, it is especially important to respect actual usage. In technical fields, there is a high rate of neologisms. It would be nice if they were all grammatical, but it is more important for the meaning to be unambiguous. Readers not familiar with resonance could easily assume the two forms refer to different things. I googled "resonan frequency" to pick up both terms, eliminated ambiguous and repetitive hits, and counted. Out of the first 44 there were 27 occurrences of 'resonant frequency' and 17 of 'resonance frequency'. I'd suggest mentioning in the article that both terms are used. --Chetvorno 10:30, 21 October 2007 (UTC)

## Split into different articles

What do people think about having this article just explain the basic idea of resonance, then have seperate articles on Mechanical resonance, Electrical resonance and Acoustic resonance? There is certainly enough of a scope to warrant splitting this article into four different articles, and I think that making four different articles would more likely encourage those who know about one specific field to expand them. --Nathan (Talk) 03:49, 30 December 2005 (UTC)

Agreed. — Omegatron 23:59, 30 December 2005 (UTC)
Right, I'm gonna do it. It seems a very logical thing to do, and one other person agrees. I don't think there's a way of moving sections (to avoid destroying the history), so I'll just have to copy and paste. I'll leave notes in the edit summaries, though.--Nathan (Talk) 01:08, 31 December 2005 (UTC)

I've done the cutting and the pasting. Now those three articles need introductions, and some of the See Also items need to be cut and pasted as well. I'll do some of it another time if nobody beats me to it. *hint* --Nathan (Talk)

## Rice resonance?

Is the link to the YouTube video actually an example of resonance and its effect on rice? It seems to me there is no reaction between the vibration of the sound and the natural vibrations of the rice but rather the rice is just creating a visual pattern of the areas of high and low vibration on the speaker surface. But maybe I'm just not clear enough on the concept.

## disambiguation

It seems like this page could be a disambiguation page, rather than pointing to a separate disambig page. It doesn't seem like this page is overpowering enough (with respect to other resonance pages) to have control of the main title. Fresheneesz 02:20, 19 May 2006 (UTC)

Resonance is important as a general concept, so it seems like it deserves its own page. A page describing Q, energy transfer, etc, seems useful, to present the overall idea. I'm not sure we need to introduce quantum field theory to do that, I'd be happy with a mechanical pendulum.

## Graphical equation question

(bkil 09:26, 12 July 2005 (UTC)) It might be useful to expand the equation
f=((T)/({rho}))^(1/2) / (2*L)=
=((T)/(m/L))^(1/2) / (2*L)
with these fractions
(+) =((T*L)/(m))^(1/2) / (2*L) =
(+) =((T*L)/(m))^(1/2) / (2*2*L*L)^(1/2) =
(+) =((T*L) / (4*m*L*L))^(1/2) =
(+) =((T) / (4*m*L))^(1/2)
ie.:

        ______
/  T   |
f =   / -----
\/  4 m L


to better visualize the relationship of the parameters, and the sentence following, that says:
Higher tension and shorter lengths increase the resonant frequency, and vice versa.

This needs to be more accessible. Telling the reader resonance in quantum field theory could be "this or that" without clarifying the distinction, or "see also [some esoteric topic]" isn't a good style. John Riemann Soong 00:47, 28 July 2006 (UTC)

I agree. The Quantum field theory section needs some serious work; it is practically incomprehensible as it is now. HEL 02:23, 15 October 2006 (UTC)
I rewrote the quantum field theory section and tried to make it less technical. If I've stepped on anyone's toes, I apologize; please let me know! The link to relativistic Breit-Wigner distribution now contains an (I hope) clear description that includes the propagator with its complex part. HEL 00:53, 20 October 2006 (UTC)

## Differential Equations?

Perhaps there should be a mention of how resonance is the result of poles in DEs, and a derivation of one of the resonant freqency formula (f=1/sqrt(LC) or some such). —The preceding unsigned comment was added by 141.213.209.215 (talk) 06:38, 17 January 2007 (UTC).

The text about quantum resonance is a copy of this text. Copyright violation? --ojs 21:07, 2 May 2007 (UTC)

Apparently so. [1] May 03, 2005 vs [2] 4 July 2005. Removed the section. Femto 13:02, 3 May 2007 (UTC)

## Triple-alpha process

I recently attended a lecture given by John Polkinghorne in which he mentioned Fred Hoyle's prediction of a resonance being required for the fusion of Helium 3 to Carbon 12. As this is a very notable example of the importance of resonance in nuclear physics and astrophysics, I have added a link in the see also section. DFH 13:12, 7 May 2007 (UTC)

Guess this is as good a place as any to point out that I removed all references to quantum field theory, etc., as this material was not directly relevant to the subject at hand (mechanical & electrical resonance). The problem is that while particle physics uses the same term ("resonances"), it does not have the same meaning as the subject being discussed here, and should not be mixed up. Separate articles, perhaps? +ILike2BeAnonymous 18:33, 8 May 2007 (UTC)

## News on this

Hi, most of you have probably seen the news that resonance is a well proven way of transferring electricity. Someone could add that? (then this article would need to cross reference Nikola Tesla too. 202.57.142.229 01:40, 8 June 2007 (UTC)

## Series Resonance circuit

I'm having a difficulty in our topic now in our subject electrical circuits. Our topic is about series RLC resonance ciruits. Our instructor told us to derive a formula on how to get the freqeuncy when the voltage of the inductor is in maximum and also the frequency when the voltage of the capacitor is at maximum.I hope you can help me out in here.I'm really having a hard time doing this. Thank you! —Preceding unsigned comment added by Marjoyumul19 (talkcontribs) 02:29, 31 January 2008 (UTC)

## On expanding the quantum mechanics section

It would be nice if someone could talk about how the Lorentzian is used in Fermi's Golden Rule when dealing with finite lifetimes. That is definitely a resonance issue. Zylorian (talk) 03:04, 8 April 2008 (UTC)

## Should "driving frequency …" read "sinusoidal driving function" in section on Theory?

My intuition is that the phrase "driven with a driving frequency ${\displaystyle \omega }$" should be rewritten as something like "driven by a sinusoidal function with frequency ${\displaystyle \omega }$", following the formula for ${\displaystyle I(w)}$ in the section on Theory.

That's my intuition, but I'm not expert enough to make the "correction" (nor do I have a reference). —Preceding unsigned comment added by W.F.Galway (talkcontribs) 14:18, 18 February 2009 (UTC)

Recently, I added a bunch of material about types of resonance in physics. Some of this was of material that was split out earlier. I am not trying to step on toes and undo the work you have done here. (I, myself, try to follow a less is more approach and try not to take expanding an article lightly.) My goal is to unify all of the oscillator articles more tightly. This is part of a larger scheme (dastardly plan?) that I have outlined in harmonic oscillator. Things that I want to do yet are: 1. figure out what to do with electric resonance. Is it just electronic oscillator and RLC, etc.. or should it include electrical resonant cavities and wave guides as well. Wikipedia is evil, editing one page leads you to another to another. 2. add a section on the quality of the resonance as determined by Q factor, damping ratio, oscillator line width, and attenuation. I am hoping for a short blurb on each and a table of the relationships between them 3. expand the lead slightly 4. clean up my mess

Number 2. in particular may be a little controversial which is why I am discussing it here. The comparison needs to be done someplace, but I am only 95% sure this is the article to do it in. It is the best I can come up with. Damping might do, but damping does not include forced motion. Oscillators may be a better place, but that redirects to Oscillation for which this discussion doesn't quite seem to fit. I want to avoid creating, yet another page to maintain, if possible.

Any ideas would be greatly appreciated. Again my main goal is to unify the oscillator pages more tightly and to make navigation and finding information more easy. TStein (talk) 06:25, 18 May 2009 (UTC)

Sounds like a great idea. It's mostly a confusing and largely unrefernced mess at this point. Dicklyon (talk) 15:51, 8 August 2009 (UTC)

## a Pendulum doesnt really resonate

true resonance requires that the restoring force be proportional to the displacement. the restoring force for a pendulum is proportional to the sin of the angle (which can be thought of as the displacement of the mass. ie. the distance it moves along its path). just-emery (talk) 02:48, 6 July 2009 (UTC)

That's true. But for small amplitudes of a few degrees deflection, which are used in all timekeeping pendulums, the restoring force is very close to linear (proportional to the deflection). Pendulums show all the characteristics of resonance: resonant frequency, bandwidth, and Q, and were the first resonant systems used by man. No vibrating system has absolutely linear restoring force, and the inherent nonlinearities in "classical" harmonic oscillators such as masses on springs is often greater than the nonlinearity of a pendulum limited to small swings. --ChetvornoTALK 05:06, 6 July 2009 (UTC)
Maybe this should be added to the end of the article. just-emery (talk) 08:59, 6 July 2009 (UTC)
I am going to leave the dubious tag up for a short while so people can commont on it. After all its only been up for a few days. However, I'm happy with the article as it now reads. I see no reason not to include a pendulum in the article as long as there is a disclaimer somewhere in the article stating that the restoring force for a pendulum is actually sin(displacement). just-emery (talk) 00:22, 7 July 2009 (UTC)
By what definition of resonance does the restoring force need to be linear? What's wrong with a nonlinear resonator? Dicklyon (talk) 15:39, 8 August 2009 (UTC)
Strictly speaking the theory of resonance comes from the solution of linear differential equations (which should probably be in this article). The resonant frequencies are the eigenvalues of linear equations. Nonlinear restoring force causes distortion, resulting in the generation of harmonics, shifting energy from one frequency to another. Only in linear systems are the energies in the different resonant modes independent of one another. --ChetvornoTALK 11:12, 28 August 2012 (UTC)
But nonlinear resonance is a valid concept, too. And the frequencies are not eigenvalues; they are parameters of eigenfunctions. Dicklyon (talk) 12:23, 28 August 2012 (UTC)
Yeah, I guess it can all be called resonance. According to Google, the natural frequencies of a system are the square roots of its eigenvalues. Do you think we should add some of this to the article? All it has is resonance curves, without saying much about where they come from. --ChetvornoTALK 13:11, 28 August 2012 (UTC)

## Theory

I'm not really familiar with the parameterization by linewidth, the use of capital gamma and omega, etc. And I'm a bit confused by the use of this "Lorentzian formula" here. The formula gives the amplitude as symmetric about the center frequency of capital omega. But the "transmissibility" or whatever it's called in the lead graph is clearly not symmetric about the center frequency -- though is is symmetric about zero frequency, which the theory formula is not. Probably these are both correct with appropriate interpretation, but I'm familiar with the form in the graph, not the other one, which appears to treat negative frequencies differently from positive frequencies. Since there's no source for this theory, I'll look for one, or replace it with a sourced one that I like better. Dicklyon (talk) 15:55, 8 August 2009 (UTC)

I think I've found the answer: this book derives the Lorentzian shape after making the "resonance approximation" that's only valid near resonance. So we should put the right formula first, then follow with the approximation for near resonance, yes? Dicklyon (talk) 16:16, 8 August 2009 (UTC)

## Resonanc stabilization from chemistry

I haven't tried to find a citation, and maybe Galileo is a good place to look, but the general principle of "resonance" is actually due to energy match or degeneracy. This attribute is what allows an oscillation mode amplitude to grow or extract energy from the driving source. In chemistry, this degenerecy of energry levels leads to stabilization, see benzene for example. I'm currently adding stuff to shape resonance and wanted a definition for resonance. Nerdseeksblonde (talk) 15:29, 14 August 2009 (UTC)

## sympathetic vibration

Aloha all

With regard to the phenomenon of drone strings. I have never been able to find an answer to this question. Would it work in vacuum? ie is sympathetic vibration dependent on a medium (air in this case).

cheers kai Makenakai (talk) 06:49, 21 September 2009 (UTC)

Will not work in vacuum. Binksternet (talk) 14:46, 21 September 2009 (UTC)
There are ways it can work in a vacuum -- sympathetic vibrations of strings if they're attached to a structure that can propagate vibrations from one string mount to the other. Some mechanism or medium of energy transport is needed, but it doesn't need to be air. Dicklyon (talk) 06:25, 22 September 2009 (UTC)
Agree with the above. For example in guitar, the vibrating strings will constantly change the tension of its support, and this will in turn parametrically drive the other guitar strings. This is different from directly pushing the strings by airwaves. --Nabo0o (talk) 18:57, 2 November 2009 (UTC)

This link in the third paragraph links to Electromagnetic radiation. Shouldn't it go to something that actually gives an example of Electromagnetic resonance like Antennas#Resonant_frequency, resonator#Cavity_resonators or similar? The word resonance or resonant does not even appear in the Electromagnetic radiation article. --220.101.28.25 (talk) 20:59, 14 December 2009 (UTC)

## Fundamental vs. Resonant vs. Natural Frequencies / Modes

Recently I've participated in several discussions which became convoluted because of misunderstandings of how these terms related to each other: fundamental frequency, resonant frequency, natural frequency, modes. If more then one of these frequencies exist for a structure and if only one exists for each degree of freedom were also unknown. Perhaps a paragraph highlighting some of this could be added? 12.188.106.66 (talk) 18:20, 17 December 2009 (UTC)

## Vibrational energy???

It will be better to use elastic potential energy. — Preceding unsigned comment added by 217.108.131.69 (talk)

The sentence refers to all forms of resonance, not just mechanical but electronic too. The point I was trying to get across was that the peculiar effects that occur in oscillating systems at their resonant frequencies (large amplitude response to small driving force, large phase changes, "ringing" transient response) occur because the system stores energy at the resonant frequency, oscillating back and forth between kinetic and potential energy, but not at other frequencies. --ChetvornoTALK 02:13, 15 October 2010 (UTC)

## Phase change on reflection

There is often a phase change on reflection, right? Shouldn't the equation take that into account? 198.109.220.6 (talk) 15:07, 8 November 2011 (UTC)

## 'Resonance frequency' vs 'resonant frequency'

An editor recently changed all instances of "resonant frequency" in the article to "resonance frequency", citing as source {{#invoke:Citation/CS1|citation |CitationClass=journal }} which points out the former term is ungrammatical. This issue has been debated above. I think, particularly in scientific articles, WP should adhere to the most common usage, rather than be guided by grammar. "Resonant frequency" is by far the more common usage. I googled the two forms and got 5,960,000 hits for "resonant frequency" versus 1,280,000 for "resonance frequency". The former term has been used for at least 170 years 1 and I doubt if it is going to become extinct now. It would be nice if the neologisms that science invents were grammatical, but the more important requirement is that they are used consistently. If there are two forms, readers (particularly nontechnical readers) may assume they mean different things. We serve our readers best by using the more common form, rather than trying to be grammar police. I think "resonant frequency" should be used in this article (with a note at top that "resonance frequency" is a synonym). --ChetvornoTALK 16:03, 24 April 2012 (UTC)

I have mixed feelings about that. If the usage were overwhelming on one side, there'd be no question, but in recent years the usage has become nearly equal (see book ngrams). How we serve our readers best is a matter of debate in this case; I can see a case for the more modern grammatical alternative. Dicklyon (talk) 16:41, 24 April 2012 (UTC)
Hunt has not been so influential as he might have wished. The "resonant frequency" is still very widely used, far more widely than "resonance frequency". I think we should go with common usage. Binksternet (talk) 17:17, 24 April 2012 (UTC)

## Pushing a swing is not an example of resonance

People who are not familiar with the idea of a resonance frequency, commonly believe that pushing a swing at the right time is a good example of resonance frequency. I would argue that it is not. Moreover, I believe that this example can lead to confusion. For example, if I push a swing every other time, the frequency I push the swing at is only half of the resonance frequency. However, the forces I apply to the swing will still add in a constructive manner, causing the swing to move higher. From this example, I may believe that the solution to a simply harmonic oscillator being driven by a sinusoidal driving function that is half the resonance frequency behaves qualitatively like a simple harmonic oscillator being driven at the resonance frequency, however, this is not true. The source of this confusion is that the force I apply to a swing is not a sinusoidal driving force.

When discussing simple harmonic oscillators, the only driving forces that have trivial solutions are sinusoidal driving forces, for example: $F(t) = \sin ( \omega t)$. Because sinusoidal functions form a orthogonal basis set, when presented with a driving force that is not sinusoidal, we can write the driving force as an integral (sum) of sinusoidal functions. This is called the inverse Fourier Transform and it is typically written in terms of a Fourier Transform. Since all driving forces can be written in terms of sinusoidal function, once we know how the simple harmonic oscillator behaves for sinusoidal driving forces, we can solve the simple harmonic oscillator for all driving forces. Because of this, we often study the solutions to the simple harmonic oscillator being driven by a sinusoidal force. The term resonance frequency refers to a frequency of a sinusoidal driving force that results in solutions that are qualitatively different than the solutions you get for other sinusoidal driving forces. Thus the term resonance frequency assumes a sinusoidal driving force. When pushing a child on a swing, you impart a short impulse to the child. Moreover, the force you apply is always in the same direction. Clearly this force is not sinusoidal. Furthermore, if this driving force were decomposed into sinusoidal forces, we would find that the component of the Fourier Transform that correspond to the resonance frequency is not much greater than the components that correspond to the off resonant frequencies. — Preceding unsigned comment added by 76.104.20.225 (talkcontribs)

Actually, it's not a bad example if presented carefully. The resonant system pretty much picks out that small component at the resonance frequency, and pretty much ignores the rest. Dicklyon (talk) 05:03, 28 May 2012 (UTC)
Yes, resonant systems are frequently driven with impulsive drive forces, as in electronic oscillators, pendulum clocks, and nuclear magnetic resonance. One of the features of a high-Q resonant system that a swing illustrates well is that it can convert a nonsinusoidal drive force into sinusoidal motion. --ChetvornoTALK 08:55, 28 May 2012 (UTC)

free vibration:When a body is distributed from its mean position and allowed to vibrate freely on its own then frequency of vibration is known as natural frequency and osicalliations are called as free vibrations — Preceding unsigned comment added by 203.194.97.194 (talk) 17:06, 7 October 2013 (UTC)