Mathcad Graph Trace Problem

I've got an older version of Mathcad, so I can't read the file you've linked-to.

The vector x_n values (the column of numbers, Mathcad will treat this as a vector) that you've provided don't seem to correspond to anything in the graph. The variable x(a) is not the same, and is treated differently than the x_n expression. I'd suggest being consistent, either express everything as x(β) or as x_β expressions. You might want to use a different letters for the functions and the variable, e.g., use b(a), b'(a) and x(a).

What are the equations you are trying to plot for a'(a) and x(a)?

Thank you for your answer. Here is the rest of the equations from the page(from the beginning to just before the previous picture):

And here is an older version 11 of the actual file:

http://dl.dropbox.com/u/10626780/Find%20a%20and%20a%C2%B4%20as%20a%20for%20specific%20x%20values.v11.mcd

sorry that it's kind of messy. I hope this makes it more clear to what i am searching for.

The x(a) functions is not possible to solve. If i was, i could have found a, and then calculated a´from it. Thats why i'm looking for another way of solving this problem.

Is there a trace functin that can give me the a and a´ values(x and y axis) from the x values(the x values follow the blue line, and is read of on the y-axis)?

Again, sorry if it is a little messy.

J.

You could define b as follows, then plug b into your equations and get exact values.

I re-wrote your equations into the old version I have (Mathcad 2000) and plotted.

Here is one of the graphs:

Here is a graph plotted with the b values given above.

Is this what you are trying to do? Does this help at all?

Hi again. I think i see where you are going. But, you are inserting the x-values(which you call b), in the equations for CP, APRIME and x. x is a function of a. a is the values i'm trying to find, corresponding the x-values. Thanks a lot for trying though! :) maybe there is no answer:/ !!

So, are you trying to find the values of 'a' which solve the equation:

x(a) = [(a - 1)^1/2*(4a - 1)] / (3a -1)^1/2 ? Is that what you are asking?

Two obvious values occur at a = 1 and at a = 1/4; both give x(a) = 0.

At a = 1/3 you get an asymptote, since the divisor goes to zero.

Or are you looking for the values of 'a' for which the curves of x(a) and C_p(a) and/or C_T(a) intersect?

Yes, i'm trying to find the values of 'a' which solve the equation:

x(a) = [(a - 1)1/2*(4a - 1)] / (3a -1)1/2

Thats the correct way to put it!

However, i know that this is not possible, since there is no obvious solution to the equation! don't ask me why!!

That is why i wanted to find some kind of grapical solution(trace, spline fit etc..)

cp and ct doesn't really have anything to do with this problem.

J.

If you redefine the limits of 'a' as follows, a:= -0.1, -0.09; 0.5

Then just graph x(a) and x(0) vs a, you get a graph that looks like:

Notice I set the graph limits at -0.05 to 0.6 in the 'a' axis and -2 to 2 in the x(a) axis.

So from earlier I mentioned that the function x(a) has two solutions, for a = 1 and a = 1/4. [The a = 1/4 solution appears on this graph where x = 0 when a = 1/4 .] If you were to then solve this equation for a in terms of x, you will get one solution, which is shown graphically at the point where a=0, which occurs when the new function a = f(x) equals zero at the point x = -1.

Right, but that still doesn't get me the a values, for the array of x-values of my original post. Thank you for your effort, I appreciate your ideas. J. :)

Okay, I finally understand what you are trying to do, I think.

Here is a solve block you can use. Since I have a different version of Mathcad, I did a screen capture and copied the image below. You'll need to type this into your version of Mathcad. You'll have to step through the values of n from 1 to 10 manually to get the xval values you are looking for. (Or you can try using a running variable and see if it will do all 10 solve values for you at once, my version of Mcad won't.) The screen capture is for the n = 10 solve.

NOTE that the greater-than-or-equals sign for 'a' and the equals sign for 'x(a)' below Given are from the Boolean menu.

Here is the screen capture:

I should also point out (in case you aren't aware) that there is a second solution corresponding to the other branch of the x(a) function when a>1. For this you'll need to re-set the limits at the start of the solve block. The expanded graph showing both branches of the x(a) function is below and the screen capture for the second set of solves is below that.

The second solution would be as shown below. For a>1 and n=1 you get a value for x(a) = 0.336 when a = 1.024393. You'll get additional values for x=n*0.336 as n goes from 1 to 10 (and beyond, for that matter).

Hello Usbport.

I was not able to do the calculations, the way you did it, but used the same method, and worked it out anyway. I think my problem was, that i did not define a before the given/find block. Thanks for doign all the graps. I'm very impressed with your persistence. You truly live up tp the saying of Richard Feynman.

J.

Have a look at http://www.uniphiz.com/digitizing.htm or http://www.digitizeit.de/

There might be others that can do the same thing for you...

If I am reading the formula correctly, the formula can be solved for a by squaring both sides and converting it to a cubic equation. You can google how to solve cubic equations in Mathcad. (multiple hits) or enter your own formula (even more hits)