Talk:Harmonic oscillator

Plagued by major errors

Hello, I've been reviewing this article closely, and noted some significant errors in content. I'll post them here for consideration before I change them, because it would constitute a major revision of the article.

In particular:

• Consider the differential equation governing forced oscillation, as currently written.

${\frac {d^{2}x}{dt^{2}}}+2\zeta \omega _{0}{\frac {dx}{dt}}+\omega _{0}^{2}x=F_{0}\sin(\omega t)\ ,$

Dimensional analysis reveals an error: The terms on the left hand side of the equation all have units of acceleration, whereas the term on the right has units of force. The right hand side should be divided by the mass.

• This error propagates through to the solution, which is incorrect (and this is dangerous if anybody relies on this solution for a design!). Z_m should be multiplied by the mass, or the force should be divided by the mass.

This article is rated as top-importance in physics! Errors like these are unacceptable.--203.140.72.237 (talk) 08:16, 20 November 2009 (UTC)

The equation is a bit more abstract than that. The section says nothing about it representing a system of mass and springs; the F is an abstract "force" for this abstract system. You could add comments that if x is the displacement of a mass, then F is force/mass, or whatever. Or go ahead and fix it to agree with how most sources (e.g. this book and this book) present it, as a moving mass. It would be great if you could clarify the relationship of these approaches, citing sources in the process (the article is desparately short on sources). Dicklyon (talk) 16:01, 20 November 2009 (UTC)

If it's an abstract "force", then the usage is inconsistent with the physics definition of "force" (ie, the F=ma kind), and this could be very misleading. I agree that it would be good for this article to cover all second-order systems governed by that differential equation, but words like "force" shouldn't be used to mean a general mathematical forcing term. What would be a good way to clarify this?--JB Gnome (talk) 05:57, 28 November 2009 (UTC)

I think $Z_{m}$ should absorb the mass term so as to be consistent with the definition of impedance given here. So it should read:

$Z_{m}=m{\sqrt {\left(2\omega _{0}\zeta \right)^{2}+{\frac {1}{\omega ^{2}}}(\omega _{0}^{2}-\omega ^{2})^{2}}}$ — Preceding unsigned comment added by 209.52.88.76 (talk) 05:51, 5 January 2019 (UTC)

Possible mistake

In the first equation in the section Damped harmonic oscillator, Fext = ..., I'm wondering if the second '=' (preceeding the "m d2x/dt2" term) isn't suppose to be a '-' instead. RDXelectric (talk) 18:32, 14 November 2016 (UTC)

I don't think so. I'm not sure about $F=-kx-c{\frac {{\text{d}}x}{{\text{d}}t}}$ (possibly another form of Hooke's law?), but $F=m{\frac {{\text{d}}^{2}x}{{\text{d}}t^{2}}}$ seems to me to just be the calculus form of Newton's second law, $F=ma$. User44654 (talk) 09:30, 25 June 2019 (UTC)

There is nothing wrong with this equation. I just supplied three reliable citations. If you would like to see the derivation, you can look up the sources.—Anita5192 (talk) 15:34, 25 June 2019 (UTC)

I didn't mean to jump into the middle of whatever this is, but I did notice on the page that the terms of that equation were showing up in certain browsers without any '-' characters separating them. It appears that characters such as '+' and '-' need to be surrounded by whitespace when they appear between ‹math› tags in order to be rendered on some browsers. I can't make any claims regarding the equation itself. Saltcub (talk) 22:40, 1 December 2020 (UTC)

Hello. Latex (Wikipedia's math markup language) has its own ideas about how to space things. Adding spaces within the Latex markup won't change anything, but can make the markup more readable. Rather than adjust the formulas for "certain browsers" it is better to adjust the browser's zoom setting. It is a never ending battle. What looks good in your browser may look bad in my browser. Some people look at Wikipedia on their phones. Basically, we stick to doing things a certain standard way and that includes letting latex control the spacing of elements in the formula. Sometimes, it is judicious to force an extra space by using the \; construct, but it makes the markup a harder to read. We don't do it for + and - signs. Constant314 (talk) 22:53, 1 December 2020 (UTC)

Thank you for taking the time to educate me on that. I can see that it's best to let LaTeX do what it wants. I don't think the issue had anything to do with browser zooming, but at any rate it seems to have been resolved now, because the '+' and '-' are now visible, even without the spaces I inserted before checking to see what the preferred style on this page is. Actually, I think I may have been confusing a misconfiguration on my computer with the Latex rendering on "certain browsers," which was a silly mistake and I won't make it again. Because of your explanation, I brushed up on Latex as well as the AMS Style Guide (which is very clear that in every circumstance, the author's preference stands except when allowing it would cause ambiguity or an inconsistency that cannot be fixed in other ways.) I see that the page is well in hand, so I'll duck back out. Again, thank you for taking the time to explain it, I really have learned from the experience. I hope you have an enjoyable December and are safe. Saltcub (talk) 22:30, 13 December 2020 (UTC)

You are not the only person to experience this problem. Wikipedia's technical wizards are aware of the problem. The last I heard from them is that they believe this was caused by a change in Chrome and certain other browsers that are based on Chrome. Constant314 (talk) 22:44, 13 December 2020 (UTC)

Literal ambiguity through uncommon notation

I have a real problem that I hope won't step on too many toes. In fact I welcome the reasoning behind why it was done this way.

So what I am concerned about is the broad inaccessibility of this explanation of both damped and normal harmonic oscillator explanations. The greet notation of ζ is used to interpret the damping ratio and is not clear an accessible for people to understand. This is not the traditional way to explain damping in physics gamma is used to equate the damping coefficient over 2 times the mass. This is never explained. You use a much more ambiguous method of getting to the interpretations of heavily damped systems that gives little derivation on what and how it relates. There is. I mention of how mass and acceleration are restated and very little use fullness in the inverted explanation of the ratio, that isn't in most university textbooks and is only readily available by shitty OCW scans. I'm flaming here but I respect the effort it takes so I'm willing to discuss why on earth a more linguistically accessible method was not performed in an encyclopedia article Saml214 (talk) 01:51, 16 April 2017 (UTC)

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Sinusoidal driving force; RFC

It should be of mentioned to students, due to so many other statements about large vibration setup, that the example Sinusoidal function :$1/m\ F\sin(\omega \ t+\beta ),$ is an impossible machine; just a rough mathematic representation (thought a useful simulator in some physics problems). This is stronger than the statement that there are "limiting factors" to infinite amplitude. When w0 approches w and r is appropriately small (the $y'[x]$ term coefficient $2\ m\ r$), A the amplitude would become infinite - infinitely possessing and outputting energy that also must be mechanically received - which is impossible. It's impossible for the input receiver to incur infinite energy without breaking. But another thing is impossible: the frequency is constant (waiting for steady state first) and the amplitude grows: which means the tip of A moves with ever greater velocity which needs to be matched by any machine to add more velocity. In real situations amplitude can grow large enough to break things (such as wind to bridge): this point is not argued. The sinusoidal "force" term, in the equations above, is purely an impossible simulation. Even for electrical wave it is an impossible machine and there is evidence of this; it's the problem with building good cutting lasers: cutting power is limited, and they melt if left operating for more than a (few seconds or minutes). A better machine can be built but not an impossible one. — Preceding unsigned comment added by 2601:143:400:547B:DDDE:287C:8883:FC69 (talk) 03:29, 16 July 2019 (UTC)

I'm not sure about the math of it all, but I'm sorry to say that the last part about lasers makes no sense. Carbon-dioxide lasers have been the standard for cutting lasers since the 1980s. The can run continuously, cutting out parts, drilling, milling, turning on a lathe, etc., all day long. Most factories can cut about anything with as little as 40 watts output power. All lasers have limits to max output-power achievable, due to a huge number of factors, ie: thermal lensing, quantum yield, reabsorption, conversion efficiency, etc... There's a limit to how large you can often scale the things up. For many lasers like ND:YAG or CO2, the primary limiting factor is often the damage threshold of the output optics. Most typical, high energy, dielectric output-couplers have a damage threshold of about 20--25 joules per square centimeter per 20 nanosecond pulse, or a little over 10 megawatts per square centimeter for continuous-wave operation. (Figure damage threshold is measured at 1064 nm, and drops in direct proportion to a decrease in wavelength, eg: at 532 nm the damage threshold will be half of the 1064 nm value.) Continuous-operation cutting powers for CO2 lasers can be in the tens of kilowatts, while some dynamic-gas pumped carbon-monoxide lasers have been reported to produce continuous outputs in the gigawatt range.

Whatever the case about the math, what we need are reliable sources that can verify what you are saying. With those, you can easily make the necessary changes yourself (just leave the laser example out.) Zaereth (talk) 22:07, 16 July 2019 (UTC)

There is no conceptual, physical, or mathematical difficulty in providing the driving acceleration $1/m\ F\sin(\omega \ t+\beta ),$ unless the oscillator is undamped, in which case the associated power grows without bound. For a damped harmonic oscillator, just some practical limits. Dicklyon (talk) 23:58, 16 July 2019 (UTC)

Hmm. That I think helps clear up what the IP was driving at. Assuming a laser cavity with zero losses along the beam path, such an intra-cavity beam would just grow and grow in intensity. Such a beam would be useless, being totally confined within the laser unit,but some mechanism would be required to release that energy before it builds up to damaging levels. (See: cavity dumper) Zaereth (talk) 00:34, 17 July 2019 (UTC)