studiot Posted September 7, 2015 Share Posted September 7, 2015 That is is this function oscillatory? Link to comment Share on other sites More sharing options...
ajb Posted September 7, 2015 Share Posted September 7, 2015 I think so by standard definitions. As the function evolves in x the sign of gradient changes back and fore. The function is exhibiting an oscillation and so is an oscillating function. The function is of course not periodic. 1 Link to comment Share on other sites More sharing options...
studiot Posted September 7, 2015 Author Share Posted September 7, 2015 It is interesting because it is nowhere periodic. I was just reading some detail from 'Quadling' who takes great pains to say this is not oscillatory, although it is alternating. I think his point is that a wiggly plot is not necessarily an oscillation. Link to comment Share on other sites More sharing options...
ajb Posted September 7, 2015 Share Posted September 7, 2015 I was just reading some detail from 'Quadling' who takes great pains to say this is not oscillatory, although it is alternating. I think his point is that a wiggly plot is not necessarily an oscillation. It is going to depend on the definition. The definition from Wolfram Mathworld of an oscillation is: 'The variation of a function which exhibits slope changes'. This is taken from Jeffreys, H. and Jeffreys, B. S. "Bounded, Unbounded, Convergent, Oscillatory." §1.041 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 11-12 and 22, 1988. The definition of an oscillation here maybe that of an alternation (or something like that) in the reference you give. Generally one has to be careful with things like this as different people will use slightly different definitions. Link to comment Share on other sites More sharing options...
Danijel Gorupec Posted September 7, 2015 Share Posted September 7, 2015 This is rutinely called 'damped oscillations'. In my mind I would call 'oscillatory' anything that has some periodic component (Probably even if it does not 'exhibit slope changes'; on the other hand I might not call something oscillatory if it does not have a periodic component even if it does 'exhibit slope changes'). Also in my mind, the term 'oscillations' might be somewhat stronger than the term 'oscillatory' (strange). Link to comment Share on other sites More sharing options...
studiot Posted September 7, 2015 Author Share Posted September 7, 2015 (edited) This is rutinely called 'damped oscillations' Actually post#1 is not a picture of damped linear or non linear oscillations. The point about ian oscillation being periodic is that a frequency can be defined. It is not possible to associate a frequency with the above plot, but thank you for the reply. Edited September 7, 2015 by studiot Link to comment Share on other sites More sharing options...
Strange Posted September 7, 2015 Share Posted September 7, 2015 The point about ian oscillation being periodic is that a frequency can be defined. Not necessarily a single frequency though. There are complex oscillations that involve multiple frequencies; like a piano string, for example, or a double pendulum. Or your graph. Link to comment Share on other sites More sharing options...
studiot Posted September 7, 2015 Author Share Posted September 7, 2015 Not necessarily a single frequency though. There are complex oscillations that involve multiple frequencies; like a piano string, for example, or a double pendulum. Or your graph Yes that's true but an oscillatory waveform, however complicated, periodically repeats itself. Incidentally I often have to remind myself to say complicated instead of complex in mathematical contexts, to avoid confusion. Link to comment Share on other sites More sharing options...
Strange Posted September 7, 2015 Share Posted September 7, 2015 Incidentally I often have to remind myself to say complicated instead of complex in mathematical contexts, to avoid confusion. In this case, both are relevant. Link to comment Share on other sites More sharing options...
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