Subject:
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Re: Off on a tangent (or a sine, anyway)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Tue, 16 Jan 2001 20:38:09 GMT
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Viewed:
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124 times
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In lugnet.off-topic.geek, Dave Schuler writes:
> In lugnet.off-topic.geek, A. Mark Wilburn writes:
>
> > If you want a wavelength of 324 and it passes through both points,
> > y = 90 cos (1.11 x) + 90 will give you the right equation. (But amplitude is
> > now 90, not 120)
>
> Doh! I was trying to be so careful! I thought amplitude was the "height"
> from high to low--is it actually half that?
Yep! It's measured from the baseline to a peak (or a valley).
> At any rate, I meant to write
> the min occurs at y=60, so that the high points occur along the line y=180
> and the low points occur along y=60. I don't mean to be difficult, but I'm
> trying to get it going from (0,180) to (162,60) in a single high:low cycle
> (whatever the term).
<grin> the term for that is half a wavelength, or Crest to Trough. Something
like that. (A wavelength is measured from peak to peak, so peak to valley is
1/2 of it).
> I've messed around a little further, and the equation:
>
> y=60cos(x/51.5)+120
>
> gets visually pretty close to what I'm looking for. Is there a more logical
> method than the try-and-try-again way I've used so far?
Yes (I just had a test on that today).
Hmmm, lemme look at it...
Alrighty, here's what you've got. Since you want a sine wave (or does it not
matter?) then the basepoint (where the wave starts) would be at (81, 120)
with an amplitude of -60 (negative coz it starts moving downward instead of
up). Since sine and cosine are the same wave, simply 90 degrees out of phase
of each other (meaning shifted to the side), your equation works fine too.
That takes care of the amplitude; now the period. A period of a normal sine
wave is 360, but you want a 324 period. So you have to put something in
front of X; which is.... hmm... old period divided by new period. Yeah. So
That's 360/324, which is 1.111 like Mark said.
Now last matter to take care of is the shift; you want the origin of the
wave at (81, 120), so you need to add 120 at the end of the equation, and
you want to shift the graph 81 to the right, so that'd mean subtracting 81
from the item you're taking the sine of.
To put that all together...
y= -60 sin(1.111x-81)+120
Which should do the trick.
Note that it's possible to orignally look at the graph as a cosine wave, or
take a different origin point, so many different equations could produce the
same graph!
> I was thinking for some reason that it should be a sine, but cosine works
> fine for me, too. Thanks for your help!
Oh, (oops, I missed this ;-)
HTH,
-Shiri
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Message has 1 Reply:
Message is in Reply To:
 | | Re: Off on a tangent (or a sine, anyway)
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| (...) Doh! I was trying to be so careful! I thought amplitude was the "height" from high to low--is it actually half that? At any rate, I meant to write the min occurs at y=60, so that the high points occur along the line y=180 and the low points (...) (24 years ago, 16-Jan-01, to lugnet.off-topic.geek)
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