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Student Support Forum: 'Plotting non-linear values and solving' topicStudent Support Forum > General > Archives > "Plotting non-linear values and solving"

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sk597653
10/23/12 10:40am

In Response To 'Re: Re: Re: Re: Re: Plotting non-linear values ...'
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Here we are, still not solved but a bit of progress made with the help of Mathematica.

The equation was not correctly cited. The paper I pulled it from placed the square root over the incorrect values. The actual equation should be:

y2 = (b - (Sqrt[b^2 - 2 k^2 c x/s]))/(2 k )

With that correction, now we are able to solve for k and s!!!

For the bad news- it does not calculate k and s to what they are known to be with a set of data that has been previously used to determine k as 2900000 and s= 0.84 with the use of SigmaPlot.

In Mathematica, the same data:

data = {{0.0, 0.0}, {0.0000079333, 0.4176}, {0.0000119,
0.5385}, {0.000015867, 0.6374}, {0.000019833, 0.7473}, {0.0000238,
0.8571}, {0.000027767, 0.9231}, {0.000031733, 0.9560}, {0.0000357,
0.9780}, {0.000039667, 0.9780}, {0.000043633, 0.9890}, {0.0000476,
1.0220}, {0.000051567, 0.9890}, {0.000055533,
1.0110}, {0.000063467, 1.0000}, {0.000075367,
1.0000}, {0.000087267, 1.0110}, {0.00010313, 1.0000}}

Using the FindFit function:
fit = FindFit[data, y2, {k, s}, x]

{k -> 1.57811, s -> 0.421896}

Why?

How does Sigmaplot get 2900000 and 0.84?

This was also done:
fit1 = y2 /. fit

2
k x -0.0000264 k x k x 2
1 + 0.0000132 k + --- - Sqrt[--------------- + (1 + 0.0000132 k + ---) ]
2 s s 2 s
------------------------------------------------------------------------ /. fit
2 k

Plot[fit1, {x, 0, 0.000098}]
which produced a graph with the straight line and the y-axis scaling from 10^-10 -> 10^-9 while the x-axis scaled 0.00001 -> 0.0001.

I did try a simple fit, such as the one you described and ws able to solve for it. My advisor suggested the same thing!

Thank you again, I look forward to hearing what you make of this.



Attachment: FindFitSOLVED shannons.nb, URL: ,

Subject (listing for 'Plotting non-linear values and solving')
Author Date Posted
Plotting non-linear values and solving sk597653 10/17/12 3:05pm
Re: Plotting non-linear values and solving Bill Simpson 10/17/12 11:22pm
Re: Re: Plotting non-linear values and solving sk597653 10/18/12 12:57pm
Re: Re: Re: Plotting non-linear values and solv... Bill Simpson 10/18/12 3:47pm
Re: Re: Re: Re: Plotting non-linear values and ... sk597653 10/20/12 4:47pm
Re: Re: Re: Re: Re: Plotting non-linear values ... Bill Simpson 10/22/12 02:06am
Re: Re: Re: Re: Re: Re: Plotting non-linear val... sk597653 10/23/12 10:40am
Re: Re: Re: Re: Re: Re: Re: Plotting non-linear... Bill Simpson 10/23/12 11:57pm
Re: Re: Re: Re: Re: Re: Re: Re: Plotting non-li... sk597653 10/26/12 4:22pm
Re: Re: Re: Re: Re: Re: Re: Re: Re: Plotting no... Bill Simpson 10/26/12 9:53pm
Re: Re: Re: Re: Re: Re: Plotting non-linear val... sk597653 10/23/12 11:09am
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