Long Sinusoid

[RichardJ]

The attached worksheet creates a "sinusoid" for which the period gradually changes with time. The way I have defined it I expect the period to start at 10 and end at 11. It doesn't though, and I can't see why. It's driving me nuts! I am sure the answer is really obvious, but I have now stared at this for so long I have tunnel vision and just can't see it. Could someone please do me the favor of pointing out what I have missed, so I can connect my aberrant neurons correctly.

Thanks
Richard

[StuartBruff]

On 12/17/2009 11:42:16 AM, rijackson wrote:
== It's driving me nuts! I am sure the answer is really obvious, but I have now stared at this for so long I have tunnel vision and just can't see it. Could someone please do me the favor of pointing out what I have missed, so I can connect my aberrant neurons correctly.

Errm, so what's my incentive for resolving this issue? It's much more fun watching someone going round the bend 😆

== The attached worksheet creates a "sinusoid" for which the period gradually changes with time. The way I have defined it I expect the period to start at 10 and end at 11. It doesn't though, and I can't see why.

Unfortunately, I don't have access to Mathcad at the moment, but could it be numeric round-off causing the problem for large multiples of sin/cos?

Can you shift the time scale so the 'last' elements effectively occur with a lower time value?


Stuart

[RichardJ]

On 12/17/2009 12:24:50 PM, stuartafbruff wrote:
>Errm, so what's my incentive for
>resolving this issue?

See below

>It's much more
>fun watching someone going round the
>bend 😆

Not if that someone goes so completely round the bend they become a seriously paranoid, foaming at-the-mouth axe murderer that does not like people that "watch them".

Richard

[StuartBruff]

On 12/17/2009 4:19:41 PM, rijackson wrote:
>On 12/17/2009 12:24:50 PM, stuartafbruff wrote:
>Errm, so what's my incentive for
>resolving this issue?
== See below
>It's much more
>fun watching someone going round the
>bend 😆
== Not if that someone goes so completely round the
bend they become a seriously paranoid, foaming at-
the-mouth, axe murderer that does not like people
that "watch them".

What, Me Worry?

Axe: Effective radius of action - 2 m
AS50: Effective radius of action - 1500 m (
http://www.accuracyinternational.com/AW50.php )

[TomGutman]

This issue has come up before, in http://collab.mathsoft.com/read?16151,10e#16151 .

Basically, your frequency (period is just the reciprocal of frequency) calculation is wrong. If you have a sinusoid sin(F(t)) you cannot get the frequency as F(t)/t. Rather you have to use dF/dt.
__________________
� � � � Tom Gutman

[TomGutman]

Here is the solution for a linear period (rather than the usual frequency) sweep. Note that while the format is MC11, the sheet does not actually work in MC11 due to the integration bug. Use MC14 for this sheet.
__________________
� � � � Tom Gutman

[RichardJ]

Yes, thanks.

Having gone and had some lunch and let my brain stew on it for a while, I now see the source of the problem. As you say, my calculation is not correct. At times close to zero though, one period is 10, so the fractional change in time over one period is large: about 10/5=2. The fractional change in the period over one period is very small: 1/50000. So although the calculation is wrong, it's very close. When the time gets up to 50000 though, it doesn't work so well. The fractional change in the period over one period is still 1/50000, but the fractional change in time over one period is much smaller: about 1/5000. So my calculation is not so close, and the period is off by about 10%.

Richard

[TheodoreM.Bones]

Write an empirical equation for the period in terms of time steps and use that in following calculations. Make it linear or higher as you prefer. A sort of parametric transformation. If you can, look at my posting LANG(2).MCD today at end for an example of parametric plotting at end of worksheet.