Exponential Problem - 13th April 2012

[LeaRebanks]

Dear All,

Please review enclosed file - Exponential Problem - 13th April 2012.xmcd

This has the full description of the problem with 3 plotted charts.

Many thanks for your help & attention.

Best regards,

Lea...

[AlanStevens]

Not sure I quite see the point (probably means I've misunderstood the problem) but how about the attached? (See just before your third graph).

Alan

[LeaRebanks]

Dear Alan,

Many thanks for your reply.

I have reviewed your input new formula for evenROOT4(t) which actually looks a little beyond my understanding of Mathcad usage. However, in any case it does not look right for what I am hoping to achieve here.

Although I think you are going in the right direction.

Please re-read the information details on No.4 discussing Plot 3 again.

I require a new function for evenROOT4(t) which has 2 adjustable components Alfa & beta.

Both of these 2 components Alfa & beta increase per time at different rates.

(My suggestion is that the Alfa increases exponentially & the beta increasing by addition of units of time.)

But whatever the setup is the end requirement from the NEW formula for evenROOT4(t) is :-

when beta = 0.25 within (2.75+beta) & with the exponential setup of the Alfa component part THEN

evenROOT4(t) = evenROOT1(t) at all points.

BUT if beta DOES NOT equal 0.25 within (2.75 + beta) then no value within the Alfa component part will cause evenROOT4(t) = evenROOT1(t) at all. And a line either above or below the evenROOT1(t) will be returned.

I hope the enclosed makes things a little clearer.

Many thanks for your help & looking forward to hearing your further reply.

Best regards,

Lea...

[AlanStevens]

Please re-read the information details on No.4 discussing Plot 3 again.

This doesn't mention anything about 2.75 + beta.

What do you mean by "within 2.75 + beta"?

evenROOT1(t) is currently just a constant times root t. Do you mean it to be a function of alpha (which is itself to be a function of t)?

The statement (beta = 0.25) returns a 1 (if beta equals 0.25) or a 0 (if beta does not equal to 0.25).

Alan

[LeaRebanks]

Hi Alan, (ADDENDUM to problem...)

Yes I should have made it more clear that the new function I desire for evenROOT4(t) should have :-

(2.75 + beta) as an essential component of the new function for evenROOT4(t)

(ii) this component of (2.75 + beta ) should be separate to the alfa component & increasing at a different rate of change to meet the desired repetitions of 2166 at the desired points as outlined in my 2 initial vectors of X & Y in plot 1.

(iii) evenROOT1(t) was only setup to show where I want the 'correct' evenROOT4(t) to plot ONLY when evenROOT4(t) has the value for beta = 0.25 within the (2.75 + beta) component.

(iv) If beta does not = 0.25 then a line just above or below the required line will be produced according to what ever value beta & alfa are set at.

I really appreciate your efforts & explanation of your formula for evenROOT4(t) but :-

(1) Your formula combines alfa & beta which is not what I want. I want separate components for alfa & beta increasing at different rates of change.

(2) Your formula does not include the component (2.75 + beta) ( my fault, I should made that clearer as above.)

(3) Your formula does not provide a plot either above or below the required line for values close to but not equal to beta = 0.25. It only produces a zero plot.

Many thanks for your attention so far.

I would certainly appreciate any further suggestions or ideas you may have to achieve my desired result.

Best regards,

Lea...

[AlanStevens]

I guess I really don't understand what it is you are trying for! If alpha and beta are functions of t, but evenROOT4 only reproduces evenROOT1 at specific values of alpha (2166) and beta (0.25) then I don't see how you can expect to make the two functions match at all values of t.

Alan

[LeaRebanks]

Hi Alan, thanks for your reply.

"If alpha and beta are functions of t, but evenROOT4 only reproduces evenROOT1 at ONE specific value of alpha (???) and beta (0.25)" - Yes this is what I want.

I want the new function of evenROOT4(t) to equal 2166 & repetitions of 2166 at n x 1, 2, 3, 4, 5, 6 points only when beta = 0.25. If beta does not equal = 0.25 then the values for alfa will cause the plot to be either above or below the desired points. In your previous function it only produces a zero line.

Ultimately, I will be trying to setup a Solve block to "extract" the desired values from the NEW evenROOT4(t) because these values of alfa & beta are unknown to me. The known points are the X & Y arrays shown.

"then I don't see how you can expect to make the two functions match at all values of t." - No I don't want this.

[RichardJ]

You want a function that when beta is not equal to 0.25 can be either above or below ROOT1t depending on the value of alpha. For this to be possible the function must have a shape that approaches that of the ROOT1t line as the function approaches the line from either above or below. If this were not the case, then the function will produce a curve that for some values of alpha will be both above and below the ROOT1t line at different points. But if it can be either above or below the ROOT1t line, has the same shape as the ROOT1t line when it approaches it, and the function varies smoothly when you vary alpha, then for some alpha it must coincide with the ROOT1t line.

The only way around the problem above would be to create a function that has a discontinuity, and jumps from one side of the ROOT1t line to the other. In which case, how big is the jump?

[LeaRebanks]

Hi Richard, many thanks for your reply. Much appreciated.

"You want a function that when beta is not equal to 0.25 can be either above or below ROOT1t depending on the value of alpha." - Correct..

"For this to be possible the function must have a shape that approaches that of the ROOT1t line as the function approaches the line from either above or below." - Sure OK

"If this were not the case, then the function will produce a curve that for some values of alpha will be both above and below the ROOT1t line at different points. But if it can be either above or below the ROOT1t line, has the same shape as the ROOT1t line when it approaches it, and the function varies smoothly when you vary alpha, then for some alpha it must coincide with the ROOT1t line." - I am sorry I don't understand your point here...

"The only way around the problem above would be to create a function that has a discontinuity, and jumps from one side of the ROOT1t line to the other. In which case, how big is the jump?" - I don't like the sound of this idea... I don't want a function that has a discontinuity, and jumps from one side of the ROOT1t line to the other.

Please review my most recent reply to Alan, above, to add more clarity to my problem.

Best regards,

Lea...

[Fred_Kohlhepp]

Not sure if this is what you want or not:

[LeaRebanks]

Hi Fred, many thanks for your reply. Much appreciated.

I have reviewed the new function you provided, but I am afraid its not want I am looking for.

Please review my most recent reply to Alan, above, to add more clarity to my problem.

Best regards,

Lea...