That is is this function oscillatory?

 

 

 

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.

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.

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.

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).

 

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, 201510 yr by studiot

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.

 

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.

 

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.