Talk:Harmonic oscillator

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Harmonic oscillator was a good article nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these are addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Reviewed version: June 23, 2006

I agree that todo lists are handy, but they belong here. Stripped from main article:

Driven harmonic oscillator: a few note about what the response of the circuit to different AC frequencies.

Damped harmonic oscillator: Note well underdamped, critically damped

Damped, driven harmonic oscillator: Notes for above apply, transient vs steady state response, and quality factor.

Mat-C 18:33, 8 Jan 2005 (UTC)

Contents

[edit] question

I have a really stupid question. Why does the potential energy equation given here look like the equation for gravitational _kinetic_ energy? and what does the kinetic energy equation for a harmonic oscillator look like? thanks--165.247.80.72 01:51, 4 December 2005 (UTC)

[edit] Random elaborations

What about adding a bit about coupled oscillators? To take a famous and interesting example, two equal masses on three springs in linear area (spring constants a,b,a respectively) exhibit two modes, fast and slow.

What about adding more about quasiharmonic and nonlinear oscillators versus harmonic oscillators? What about links with the pendulum equation \ddot{x} + \sin(x) = 0?

What about symmetry breaking? Example (might better go in article on pendulum equation): take a pendulum swinging from a sliding bead on a frictionless rod, with bob and bead having same mass. Compute symmetry group. Now provide the sliding bead with a restoring force (spring with spring constant a). This breaks some symmetry (new point symmetry group subgroup of previous). ---CH 23:31, 15 March 2006 (UTC)

[edit] Technical Error

In the section titled "Damped, driven harmonic oscillator" there is an error in the equation introduced by: One might see that for a certain driving frequency, ω, the amplitude (relative to a given F_0) is maximal. This occurs for the frequency

The equation gives the frequency for the oscillitory part of the transient solution, but that is NOT the maximum of the driven resonance. The maximum of the driven resonance occurs when ωZ_m is a minimum, and that occurs for ω^2 = k/m - r^2/(2m^2).


199.106.52.17 00:43, 19 April 2006 (UTC) SRS

[edit] Fourier transform method is missing

There should be a section showing how to deal with the oscillator equations by using Fourier transforms. It is an extremely powerful tecnique and actually makes the physics easier to understand.

Agreed.... Try a general solution as a fourier series of harmonic vibrators: ΣAneiωnt. Transforming to the frequency domain not only makes life a lot easier, but can account for loss (imaginary component) . BrintCorb 04:02, 14 August 2006 (UTC)

Do we have a young Einstein here on Wikipedia?

Before trying to add more and more complex equations, it's needed first to explain these motions with a more accessible language. For example, you can obtain the X=A cos (ωt) formula first with geometrical methods, then by solving the differential equation and finally with the advanced mathematical methods like Fourier or Laplace transforms. What do you think? --Twicemost (talk) 23:03, 3 February 2008 (UTC)

[edit] GA failed

For these reasons :

  • If we define [FORMULA] , then the equation can be written as follows ... where does this equation comes from? ... is it angular velocity?
  • It is a bit harsh to be in an encyclopedia with half the variables not defined. It would be nice for a physics book but it is tough to understand for neophytes.
  • Needs wikilinks for words like nonhomogeneous, second order, inductor-capacitor , etc.
  • Not enough references too.
  • Too many formulas for the amount of prose. Lincher 15:11, 23 June 2006 (UTC)

[edit] Merge the two Simple Harmonic Oscillator sections?

There are two distinct section "simple armonic oscillator" that say more or less the same things in different ways, someone should merge them.--Pokipsy76 08:09, 28 October 2006 (UTC)

There are two sections named "Simple harmonic oscillator", of which I found the second one is somewhat redundant as it looks similar to the first one. Also, the second one is not so related to the above paragraph and the following one. Therefore, I suggest the second one should be merged into the first one.--Kris Huang 05:57, 22 July 2007 (UTC)

I concur. --Chetvorno 22:52, 13 August 2007 (UTC)

I agree. The second section is very confusing and redundant. --Tweenk (talk) 11:04, 14 December 2007 (UTC)

[edit] Impedance vs linear response function

Reference is made to impedance, an article which does not exist yet. If just written an article on linear response function and added a corresponding link here. What about deleting the link impedance? --Benjamin.friedrich 15:35, 13 December 2006 (UTC)

There is now an article on Electrical impedance ... also fixed link in Benjamin.friedrich's comment because it pointed to a disambiguation page which causes it to show up on a database dump for things to fix :-) --mlewis000 18:59, 21 December 2006 (UTC)

[edit] Amplitude and phase

The article says:

" x = A \cos {(\omega_0 t + \phi)} \,

where the amplitude A \, and the phase \phi \, are determined by the initial conditions."

Should the article say how are the amplitude and the phase determined by the initial conditions?

If the initial displacement is x(t0) and the initial velocity is v(t0) what are the amplitube and the phase?

Glome83 17:22, 4 June 2007 (UTC)

[edit] Q

I'd like to see at least a brief mention of the Q of a harmonic oscillator. In addition to extensive use in engineering applications, it is run into regularly in physics. It's one of the most common characterizing statistics of underdamped resonant systems (Why is an atomic clock a better timekeeper than a quartz crystal? It has a higher Q). --ChetvornoTALK 09:03, 25 November 2007 (UTC)