Talk:Simple harmonic motion

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Slight change in formula[edit]

Hi...I'm new to editing wikipedia.....pardon me if something is wrong I changed reference 1 because of incorrect furmula stated there The original formula is Cosx = Sin (x-pi/2) which is wrong. The correct formula is Cosx = Sin (pi/2-x) —Preceding unsigned comment added by (talk) 17:26, 31 March 2010 (UTC)

Possible Vandalism[edit]

I failed to log in before jumping into repairing a severe error in the Useful Formulas section. Someone had written the equation f=A/t, where they had listed t as the period, even though T was already serving that purpose. This equation is faulty for two reasons: First, frequency is independent of amplitude for simple harmonic motion. Second, the units in that equation don't even match. I see some records of vandalism, perhaps this article should be edit-restricted.

  • I also pasted in statements in both the mass/spring and pendulum sections just after T is derived asserting that the equations dictate that period is independent of amplitude (and of gravity for mass/spring, and of mass for pendula).

--Tibbets74 (talk) 06:05, 30 November 2008 (UTC)


Simple Harmonic Motion is the bomb. IT GOES BOOOM!

Great article! Very comprehensible! I like the example with the record turntable.

A pendulum DOESN'T exhibit simple harmonic motion, only periodic motion. The acceleration towards the center depends on the sine of the distance from equilibrium rather than the distance itself. I've never heard of this 'pulsation' explanation (I think you mean period)...

(The sentence in the article in question is best interpreted to mean that a pendulum approximates simple harmonic motion when the angles are small)

SHM points to this article. However, shm also stands for "shared memory" in computer science.

The formula for frequency is never directly and simply stated, which can be confusing. It can be solved for from the formula for omega and the information given, or from the formula for period and the information given, but I believe it is the article's role to show the formula directly. A discussion on what omega, in this context, really means, would also be useful. I do not know myself, and therefore cannot write it, but I am immensely curious.

IMO it would be better to define 2*pi*f / 2*pi/T as omega early on, then use it in the general equations x(t) and v(t), making them a bit easier to read. Any objections? 18:08, 4 January 2007 (UTC)

Some changes[edit]

This got too long to put in an edit summary, so the summary is here instead.

  • Took the above suggestions to explain frequency early on and to use angular frequency more extensively.
  • Replaced gamma with delta, which is a far more common symbol for the phase (I've never actually seen gamma used).
Actually, all the books and references I've seen have used Phi for the phase shift. Delta, I thought, was used more for differentials and displacement (i.e. "Change in..."). Andrew (talk) 12:51, 27 November 2007 (UTC)
  • The bit about energy was moved from the "Mathematics" section to the "Realisations" section, and removed unnecessary qualifiers. Plus, A in that expression is the amplitude, not the mean displacement (which is zero).
  • Surely there's a better word to use than "realisation" -- any suggestions?
  • There is no exact solution to the swinging pendulum: it gives an elliptic integral.

Anarchic Fox 22:22, 4 July 2007 (UTC)

Possible Changes[edit]

I would suggest using the definition of simple harmonic motion as acceleration proportional to extension from equilibrium position as a starting point in order to DERIVE that x = asin(omega.t+delta). This seems more logical rather than seemingly plucking that equation from nowhere; it is much easier to understand the acceleration definition and then integrate to get position, although of course the mathematics are a little more taxing. Anyone object? Rudipoo 20:40, 16 September 2007 (UTC)

Simple harmonic motion occasionally appears in situations where acceleration is not needed for the discussion... for instance in circular motion. I don't object to acceleration as a starting point, though. Anarchic Fox 03:55, 4 October 2007 (UTC)

Might it be an idea to remove the comma out of the acceleration equation - it currently looks like  a(t) = -\left( 2\pi ,f \right)^2 x(t) . I personally think it should not have the comma there, as the two terms are multiplied so can be written one after the other, i.e.  a(t) = -\left( 2\pi f \right)^2 x(t) . The6thhiddenimage (talk) 12:08, 23 January 2008 (UTC)

May I suggest that someone take a look at Note 2? There seems to be a coding error, as the last part of the statement about xmax = A. has been moved over into the area under the graphic. There is now an overlap between the statement and the comment of the graphic. I tried to fix this, but no matter what I did, at least the A stayed over under the graphic. Can someone fix this? (Non-user) 01:53, 8 December 2010 (UTC)

An addition[edit]

This article is good but can someone please label all the variables and what each means because just giving the equation without stating what each variable means or defines is very confusing and pointless for an encyclopedia to publish or show so others can learn when the people reading the formulas have no idea what the variables stand for. Thanks —Preceding unsigned comment added by (talk) 02:36, 29 November 2007 (UTC)


Please be careful. Earlier the differentiation of cosά was shown to be sinά whereas it actually is -sinά. - Manik (talk) 20:42, 3 January 2008 (UTC)

!It would be nice if established standard notations are used rather than abruptly using english characters to denote quantites like frequency, just for the sake of convenience. -Manik (talk) 21:19, 3 January 2008 (UTC)

Topic is introduced at too technical a level[edit]

This article introduces the subject at too technical a level. SHM is an important introductory kinematic concept and is introduced in elementary algebra classes as the projection on the coordinate axes of an object moving in a circle about the origin, long before harmonic oscillators and Newton's equations. In Wikipedia, SHM is referenced in many basic articles that don't have anything directly to do with harmonic oscillators, such as Phase (waves), Angular frequency, Wave, Sine wave, Curve, Lissajous curve, Motion (physics), Vibration, Eccentric (mechanism), Crank, Reciprocating motion, Time in physics, Trigonometric functions, and Exponential function. I don't object to including explanation of harmonic oscillators as the ultimate source of SHM, but the article needs to start with a simpler explanation of SHM as a function of circular motion, and detailed definition of the three parameters in the SHM expression: amplitude, frequency, and phase. We technical editors need to recall our own school days, and remember that the vast majority of readers of this page are nontechnical people who merely want the simplest, most elementary explanation of SHM. --ChetvornoTALK 07:15, 20 October 2009 (UTC)

Oddly enough, approaching the subject from both less technical and more technical levels uses the same idea of projection of circular motion. At the more technical level invoking the complex plane, one begins from the fact that ωt traces a steadily rotating point around the unit circle when ω is any complex number on the unit circle, such as -1, jx for any real x, or xj for any positive real x such as e or eπ. The even and odd derivatives of ωt are respectively its real and imaginary parts, each with its own scale factor. Phase and frequency are determined by choice of origin and scale of t respectively. When ω = 1 the phase and frequency of ωt are zero.
Forty years ago I asked Martin Gardner why he never used complex numbers in his Scientific American column, and he said he considered them beyond the scope of his column. Given how advanced some of the other concepts were in his column, I felt this was short-changing the Sc.Am. readership by perpetuating an unfortunate stereotype aggravated by the pejorative terminology "complex" and "imaginary" when all that was really involved was the harmonious marriage of geometry and algebra obtained by taking j to be the algebraic representation of a 90-degree rotation of the real axis about the origin. Rotation by a given angle is represented algebraically as multiplication by the value of ω on the unit circle representing that angle. When ω = j, it is obvious that the product of two rotations by 90 degrees maps 1 to -1, and more generally each point in the plane to its reflection in the origin.
It is ironic that high school education has given more latitude in recent decades to sex education than to complex numbers. If instead of viewing complex numbers as something to be feared, as this article evidently does by not even daring to mention their name, they were presented as both beautiful and beneficial, it would eliminate one of the demons contributing to math anxiety. --Vaughan Pratt (talk) 19:05, 27 September 2011 (UTC)
I wasn't objecting to the use of complex numbers in describing SHM, but to its definition as the motion of a harmonic oscillator, requiring differential equations for readers to understand. It should be defined first in an introductory section for nontechnical readers as the projection on the axis of a point moving in a circle. --ChetvornoTALK 22:31, 27 September 2011 (UTC)

Formula change[edit]

Shouldn't v(t) be equal to -Aw sin(wt) rather than +Aw sin(wt) ? — Preceding unsigned comment added by (talk) 19:27, 26 March 2012 (UTC)

Too many big words.[edit]

Perhaps I'm merely beholding a stance endemic across myriad scientific disciplines; but in my opinion, characterization of this article as simple, specifically through use of the moniker "simple" in the title "Simple English Wikipedia," conveys to those ill-versed in the technical jargon an impression of out-of-touch arrogance on the part of the authors. I therefore respectfully submit that inclusion of a gloss of the definitions of the technical terms used in this article could make great strides in elucidating readers who under varying circumstances are possessed themselves of a vocabulary lacking in the requisite degree of sophistication.


Maybe this is a problem in all science; but calling this article simple, by naming it "simple" in the title "Simple English Wikipedia," makes the authors seem snobby to readers who actually need simplicity. That's why I think adding definitions for the technical terms used could make things far more clear for readers who for whatever reason have a limited vocabulary.


I think use of small vocabulary in the Simple English Wikipedia is important because the English and Simple English Wikipedia, being written in the lingua franca of the Internet, hold a unique potential to facilitate transmission of knowledge into Wikipedias that currently serve underserved populations.

Wikipedias written in languages which are a linguistic minority in their jurisdictions could serve wholesale as a model for use of the minority language in online communications. By helping a language make the transition into online communication, a feedback loop could be created bolstering the utility both of the minority-language Wikipedias and of the languages those Wikipedias serve. This would in turn allow more people to in good conscience teach their mother tongue to their children, which could in turn inspire use of the language in literary and cultural pursuits, or ultimately perhaps prevent foreign linguistic domination and/or language death.

This potential is decreased when articles use relatively-opaque technical terms. (talk) 04:42, 13 December 2013 (UTC)

??? This article is not in the Simple English Encyclopedia. Dicklyon (talk) 06:33, 13 December 2013 (UTC)
The word simple refers to the harmonic motion as such, not to the article difficulty. Compare complex harmonic motion. Isheden (talk) 13:47, 13 December 2013 (UTC)

I also find the article confusing. Some examples of non-harmonic motion might help. How is harmonic motion different from periodic motion? Verycarefully (talk) 19:40, 15 May 2014 (UTC)

The first sentence explains that SHM is one particular type of periodic motion. Another way of explaining would be that periodic motion is simple harmonic if the displacement (and therefore speed and acceleration) varies sinusoidally with time, but I don't think that's a simpler way to explain the motion. I suppose we do get readers with no background in either mathematics of physics, but it is difficult to explain without using the vocabulary of those disciplines. I might have a go at creating an article in Simple Wikipedia, but it's not easy to do in words of one syllable. Dbfirs 16:31, 16 May 2014 (UTC)
Really, Dbfirs? You don't think that's simpler than differential equations? The reason it is unnecessarily complicated and confusing people is that the article introduces the concept the wrong way. See Topic is introduced at too technical a level, above. SHM is just sinusoidal motion, defined by the motion of the projection of a point moving in a circle 1, 2 approximately the motion of a piston in an engine, or a person's leg pedalling a bicycle. It doesn't necessarily have anything to do with a harmonic oscillator, restoring force, Hooke's law, or differential equations. Elementary texts normally introduce it that way, long before harmonic oscillators 3, 4, 5, 6, 7. This article should first define it that way, as the projection of a point moving in a circle, and then introduce the sine function and present the equation of SHM
x(t) = A\sin(\omega t + \phi) \,
And then in a subsequent section explain its connection with harmonic oscillators. Unbelievably, this gobbledygook article doesn't even include the basic SHM equation above until the 3rd section, and then doesn't explain the parameters A, ω, φ, the core of SHM. It represents the triumph of the editors' desire to show off their skills at solving simple linear differential equations over their desire to write an understandable article. --ChetvornoTALK 21:00, 16 May 2014 (UTC)
Yes, I do think that is simpler than differential equations, and I would expect the Simple Wikipedia article to explain it in this simple way. I'm also happy to have a simpler introduction in this article. Dbfirs 09:27, 24 May 2014 (UTC)
Sorry, Dbfirs, I was uncollegial. Must have been those 20 cups of coffee I had :) --ChetvornoTALK 10:23, 24 May 2014 (UTC)
No offence taken. Perhaps I should have been more critical of the article, but I decided that my "sinusoidally" was not a simple word, whereas a weight bouncing on a spring can be imagined by most people, and a statement of the conditions under which SHM occurs can be expressed in simple English. I started a simpler article on Simple Wikipedia, but I'm not into creating animations, and a (moving) picture is worth a thousand words in this context. Any .gif experts? Dbfirs 12:16, 24 May 2014 (UTC)
I'll see if I can make something. --ChetvornoTALK 18:01, 24 May 2014 (UTC)
Thanks. My simplest bicycle explanation ended up as cycloidal instead of sinusoidal, so I abandoned it! Dbfirs 20:54, 24 May 2014 (UTC)
Hey, maybe it can be reCYCLEd at cycloid (sorry) --ChetvornoTALK 03:10, 25 May 2014 (UTC)
Here's a first stab at a SHM animation. I don't have much experience, I guess there are a lot of ways it could be done. Thoughts? Corrections? Improvements that should be made? --ChetvornoTALK 03:10, 25 May 2014 (UTC)
Simple harmonic motion animation 1.gif
Yes, that looks good. Thank you. Possibly slow it down a fraction? (There's already a good cycloid animation.) Dbfirs 06:36, 25 May 2014 (UTC)
Yeah it is too fast, I'll slow it, thanks --ChetvornoTALK 07:23, 25 May 2014 (UTC)
A version showing both sine and cosine motion. --ChetvornoTALK 19:17, 25 May 2014 (UTC)
Simple harmonic motion animation 2.gif
The cosine one needs some mental gymnastics (easy for those accustomed to it) to rotate the displacement 90 degrees, but it's also a plot of the velocity (for omega = 1). May I use your simpler version for Simple Wikipedia? Dbfirs 20:00, 25 May 2014 (UTC)
Sure, I think that one's better too. --ChetvornoTALK 21:30, 25 May 2014 (UTC)


Sine and cosine animation.gif

If you have any suggestions for improvement, different axis labels, etc., or ideas about a different way to present the concept, I'd be glad to take a shot at it. One defect of these diagrams is that they don't include the phase factor φ. I was thinking of making one where the circular motion, and the sine wave, doesn't start at ωt=0, but it may confuse newbies, because the single period sine wave will no longer have the familiar form. --ChetvornoTALK 21:55, 25 May 2014 (UTC)
Another animation that shows both sine and cosine:
--ChetvornoTALK 00:16, 28 May 2014 (UTC)