Les

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These are questions asked by Les

I am attempting  to show that ocean wave B has a larger velocity than ocean wave A, because wave B has a longer wavelength.


 

I considered the displacement of two particels located at the peak of each wave at time = 0.  Differentiating the two displacement functions I determined the velocity function for each particle.  I used a sequence to determine the velocity for each particle over the time interval 1 to 20 seconds (integer).  The following syntax produces the information I need but I would like to format it as 3 columns in 20 rows, how could I edit the following syntax to do that?

restart;
R := {seq([t, evalf(-sin(t)), -.5*sin(.5*t)], t = 1 .. 20)};

This sequence prints 20 lists of t, evalf(-sin(t)), -.5*sin(.5*t)

What do I need to do to print 3 columns in 20 rows?

The first 3 rows would look something like

1 -0.84147 -0.23971
2 -0.9093 -0.42073
3 -0.14112 -0.49874

I am trying to show that two ocean waves of equal amplitude but different wavelenghts have different velocities and the wave with the largest wavelength will have the greatest velocity.    If someone has a suggestion about how to show this using SHM, any advice welcomed.

Les

 

How do I plot the following with Maple 2015?

The attached worksheet performs two functions:

(1) It lets me print 4 × 6 Index Cards for the short entries in each table.

(2) It allows for easy storage and retrieval of syntax (code).

The worksheet has many tables, each separated by a Page Break.

Questions:

(a) Is there a way to sort all the different tables so they will be arranged in alphebetical order?

(b) When I select one table to print and open the Print Dialog, the "Selection" option is grayed out. (see graphic below).  (1) Is there a way to enable the selection option?  (2) Is there a way to determine what page I am on so I can use the "Pages from...to" option?  If I need to number the pages, will the page numbers reset to parallel a new alphabetic sort order.

Many thanks in advance.  See WC29_4_BY_6_NOTE_CARDS_UNSORTED.mw attached. And see image of Print Dialog below.

Les

Could someone help me with the following.  The syntax produces an unfinished graph with a warning.

> with(plots);
> z := polar(1.05, (1/10)*Pi);
                             
> display(polarplot(1, color = grey, axis[radial] = [color = "Blue"]), complexplot(seq(evalc(z))^n,
n = 1 .. 21));

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

the graphic looks like this

The graphic should look like this

Thanks, any help appreciated.

Les

 

Maple 2015

Using with(combinat) the permutation of {a,b,c} is determined.

>restart:
>with(combinat):
>permute({a, b, c})
                  [[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]]

The tree diagram of this permutation is

    

In Maple, using with(combinat) and with(GraphTheory), when I attempt to draw the permutation I get the following error:

>L := permute({a, b, c});
       L := [[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]]
>DrawGraph(L);
  Error, invalid input: GraphTheory:-DrawGraph expects its 1st argument, H, to be of type       {GRAPHLN, list(GRAPHLN), set(GRAPHLN)}, but received [[a, b, c], [a, c, b], [b, a, c], [b, c,      a], [c,   a, b], [c, b, a]]

On Maple, again using with(combinat) and with(GraphTheory) the command permute(3) is used.  The results are manually configured as node-connection lines.  A fair representation of the tree diagram is configured by Maple, although the diagram has numeric instead of alpha configurations, and the a,b,c structure shown above is not easily recognized.

Any suggestions on developing a procedure that will graph (draw) an alpha-labeled permutation welcomed.  Thanks!  WC44_Permutation_Graph.mw

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