Talk:Simple harmonic motion

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Slight change in formula

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 122.173.206.27 (talk) 17:26, 31 March 2010 (UTC)[reply]

Possible Vandalism

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)[reply]

BAD

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? 80.169.64.22 18:08, 4 January 2007 (UTC)[reply]

Some changes

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)[reply]

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)[reply]

Possible Changes

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)[reply]

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)[reply]

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)[reply]

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 x_max = 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

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 72.39.14.126 (talk) 02:36, 29 November 2007 (UTC)[reply]

Formulae

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)[reply]

!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)[reply]

Topic is introduced at too technical a level

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. --Chetvorno^TALK 07:15, 20 October 2009 (UTC)[reply]

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 ω^t traces a steadily rotating point around the unit circle when ω is any complex number on the unit circle, such as -1, j^x for any real x, or x^j for any positive real x such as e or e^π. The even and odd derivatives of ω^t 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 ω^t 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)[reply]

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. --Chetvorno^TALK 22:31, 27 September 2011 (UTC)[reply]

Formula change

Shouldn't v(t) be equal to -Aw sin(wt) rather than +Aw sin(wt) ? — Preceding unsigned comment added by 89.211.134.249 (talk) 19:27, 26 March 2012 (UTC)[reply]