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A classical math problem: differential equations

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Here is the Mathcad 11 sheet that solves nth order differential equations with constant coefficients, referenced in the document thread with similar name here: A Classical Math Problem from a Classical Text (Differential Equation).

 

Note that this, as it is, is NOT usable for:
- Systems of differential equations,

- Differential equations where the coefficients of the derivatives are not constants (when they depend on t).

 

But in both cases, similar techniques can be used to solve specific systems.

 

Luc


Region Border Glitch

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Not sure if this is a glitch as such, however, when I have switched off show border for region, it still shows up in print preview and when printing.

 

Has anyone else experienced this?

 

 

Thanks

How to solve a symbolic equation for vibration system

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Hi, friends.

 

Is there a way to solve the symbolic solution for a vibration system in mathcad?

Capture.JPG

Such as f(t)=0, and the solution should be in the form of Asin(wt+a)+Bcos(wt+a)

 

Thank you in advance!

Looking forward to your help!

 

Shawn

Why does mathcad forget units?

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Unit problem.JPG

 

Hi!

 

I can't find the reason why mathcad leaves the unit in the last row "y=5.5x10^7".

Mean value of only few columns in a Matrix

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Hello,


I need a little help in mathcad program to get the mean values of few columns(every third column) in a big m*n matrix. See  the attached image for description.


I want to find the mean of highlighted columns, What I did now is I wrote a program to pull the highlighted columns into a new matrix and then I wrote an another program to find the mean of values in every row.

 

I wonder if there is any way to find the mean of intermediate columns using one program without pulling these values into a new matrix and have an another program to find the mean for all the rows in that matrix.

 

I could have attached my program file here but unfortunately I don’t have MathCAD in PC write now. Curious to get the answer by the time I go to my work tomorrow

 

Thanks for your help!!


Ashok

Nonlinear curve fitting of piecewise-defined function

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As suggested by the title, I'm attempting to fit a piecewise-defined curve to a set of data points.  This is also the first time I have used Mathcad, so it is exceedingly likely I'm missing something obvious.  My worksheet is attached to this post.

 

I'm attempting to follow the example at http://www.phys.uconn.edu/~hamilton/phys258/P/genfit.pdf, but when I call the genfit routine, I get the error "This value must be a function".

 

So, question number 1: what is this error message trying to tell me, and how can I resolve it?

 

While I have your attention, I also have question number 2.  The function is a horrible mess because I'm trying to combine data points with continuity restrictions.  I don't know how to specify symbolic relations between fitting parameters (e.g. forcing the second derivative to be continuous at x = 60 yields "e = b + 24").  So I've solved the continuity restrictions by hand and substituted them back in.  Is there a way to get Mathcad to recognize additional restrictions on the fitting parameters beyond just the list of data points?

 

And branching further afield still, question number 3: can Mathcad do symbolic differentiation of piecewise functions?  When I ask for d/dx(f), I get an error message that f "must be a scalar".

 

Thanks in advance for any help you all can offer.

Backsolving springs with known lamdas - 4x4 Matrix Determinant

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I have a mass-spring system.  I am trying to back-solve four springs (provided in the attached file).

 

There are four masses at which summation of forces are performed and A matrices are obtained.  The attached file shows them in the (Lamda*I - A) format. These springs and masses are configured in four different ways and their first mode natural frequencies are known.

 

Therefore, in my mind, I should be able to use Given/Find in order to find the unknown springs with four equations while setting the determinants of the four matrices to zero.

 

The solver doesn't converge.

 

What is the problem here?  Can this be done?  If not, how else?

 

Your help will be greatly appreciated.

 

Thanks,

 

Eric

One phantom part of the curve


Trial and error

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Hi,

 

I am trying to get a solution in mathcad in which we provide a specific value (say 0) initially followed by set of equations and finally giving result.

But if the result obtained is <> zero, program will automatically change the initial value until we get the final result (by trial and error) as or nearly zero.

 

 

this is one example.

Trial and error.jpg

 

Please help me solve this using Mathcad.

 

Thanks.

Multiple integration Problme

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I want to integrate the following expression in mathcad.

Untitled.png

the answer should be the following if p(r)=po=constant

Untitle11d.png

But when i try to solve this expression in mathcad i get this:

Untitleffd.png

It should give 64 instead of 24. What am i doing wrong.?

Polynomials

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Does mathcad calculate all polynomials with numerical math or do they have an exact result. Thank you for answering.?

the requested file is not a valid mathcad xml worksheet

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Hello,

 

I have seen that similar topics were opened but I could not find a solution to my problem. So sorry if the solution of this problem was explained somewhere in the ptc community and I missed it.

 

I have a problem opening a file that I created a couple of days ago. I was using Mathcad 14 but I haven't checked which version to be honest. I typed the solution of an exercise that we gave in the class to the students and when I was done I saved the file as "xmcd". In order to send to some colleagues I also saved the file as ".rtf". I wanted to add some comments in the solution. So I tried to open the .xmcd file again but I got "the requested file is not a valid mathcad xml worksheet" error. For the last 2 days I have been trying to find a way to open the file. I tried to uninstall and install Mathcad 14 but it didn't work out. Some people in other topics suggest that upgrading the version might help. I installed Mathcad 15 with free trial license and still cannot open the file.

 

Could you please help me to fix this if you encountered the same problem before? The solution of the exercise is about 15 pages and I invested a lot of time on that. So I would be very very glad if you help me to find a way to fix this.
I am attaching the mathcad file that I am having problem with.

 

Thank you in advance.

Operations on Nested Matrix

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I created a set of equations that calculates the positions of the two masses with a couple of springs: one to the ground and another between them.  The result looks reasonable as it shows below:

 

 

Now I am actually performing a tolerance analysis and there are 18 different conditions in a 9x2 matrix.  I vectorized all statements and got as far as it shows below:

 

 

Rightfully so, each element in the vector has 9x2 matrix nested.  How do I access a particular vector corresponding to a condition?  For example, how do I plot one vector or all vectors?

How to constrain the solution as an integer in Solve Block?

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Hi, everyone,

 

Is there a way to have an integer constraint in solve block?

Say, the solution is in form of sin(t) or cos(t), I want to check the maximum values after several periods.

 

Please see attachment.

 

Thank you very much.

Shawn

Plot fails when inputs have units? Please Help!

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Hi, everyone,

 

For a vibration SDOF system, when I defined the units for variables like spring stiffness, mass, damper constant...

Mathcad tells the plot fails, but when I delete the units, it succeeds.

Please see the attachment for both cases.

 

Looking forward to your help.

Thank you

Shawn


Find minimum non zero value in a matrix

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Hi, is there an easy way to find the non zero minimum in a matrix?

Or is a loop the only way to do it?

This is what i have at the moment.

nonzeromin.png

VERY IMPORTANT: Critical issues with Mathcad 15.0 M040 in handling matrices with 256 or more elements.

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Hi,

 

I recently open the download section on PTC's site (link: https://support.ptc.com/appserver/auth/it/esd/product.jsp?prodFamily=MCD ) and see the following message:

 

"VERY IMPORTANT: Critical issues with Mathcad 15.0 M040 in handling matrices with 256 or more elements.

 

Please refer to

CS218119 - Warning: an unrecoverable read error has occurred. xx regions could not be read from this document while opening specific worksheets in Mathcad 15.0 M040: http://support.ptc.com/appserver/cs/view/solution.jsp?n=CS218119

CS217297 - Error "Operation aborted: max-element-depth constraint violated" occurs when evaluating big matrices in Mathcad 15.0 M040: http://support.ptc.com/appserver/cs/view/solution.jsp?n=CS217297

 

PTC will release a new maintenance release Mathcad 15.0 M045 that would address these issues soon."

 

Pic_1.png

Optimization Series - Lesson 06

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I am sharing a list of exercises on optimization. The course required Matlab skills, but I am doing it on Mathcad. Until now I didn't have problems.

Any recommendation to improve optimization skills on Mathcad is welcome.

Regards.

 

I am still working on the list of exercises attached, for now I have just a sketch. When I finished it I can post the solutions.

Optimization Series - Lesson 03

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I am sharing a list of exercises on optimization. The course required Matlab skills, but I am doing it on Mathcad. Until now I didn't have problems.

Any recommendation to improve optimization skills on Mathcad is welcome.

Regards.

 

The attached file was built on Mathcad 15.0 .

Optimization Series - Lesson 05

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I am sharing a list of exercises on optimization. The course required Matlab skills, but I am doing it on Mathcad. Until now I didn't have problems.

Any recommendation to improve optimization skills on Mathcad is welcome.

Regards.

 

The attached file was built on Mathcad 15.0 .

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