Mathematica: Regarding ListPlot and Manipulate

[Kortirion]

I am having trouble with ListPlot in combination with Manipulate. I can't see why it doesn't do what I tell it to.

What I'm trying to do: I have several functions that is dependent upon one parameter t. These functions I got from solving a system with DSolve. I'd like to see their values varying with this parameter t next to each other like amplitude spikes, spaced 1 apart on an axis (not the t axis!).

What I did: I tried using the Manipulate command like this

Manipulate[ListPlot[{
0.02 t^2,
0.4 t,
Abs[Subscript[y, 5][t] /. solution[[1]]]^2,
0.4 t,
0.02 t^2},
Filling -> filling, PlotRange -> All], {t, 0, 25}, {filling, {None, Axis, Top, Bottom}}]

here on place 3 is one of the functions that I'd like to see varying with t, and the other four places is just filled with some "whatever" functions.

What I get: I get the anticipated evolution of all those "whatever" functions, although nothing for the one in the middle at place 3. This is strange to me! Since I can successfully plot the function alone in t like this

Plot[Abs[Subscript[y, 5][t] /. solution[[1]]]^2, {t, 0, 75}]

But in the above Manipulate and ListPlot I have a total blank on place 3.


Someone feeling handy today?

 

[Bill Simpson]

This is a wild guess here.

I'm thinking you believe ListPlot means plot this list of functions.

I believe Mathematica thinks ListPlot means plot this list of data points.
http://reference.wolfram.com/mathematica/ref/ListPlot.html?q=ListPlot&lang=en
I do not believe ListPlot creates lists of points for you.

Perhaps try
Manipulate[Plot[{
0.02 t^2,...

and see what you get.
Plot[{a list of functions}
should plot that list of functions on top of each other.

OR

Temporarily throw away your Manipulate and just see what

ListPlot[{
0.02 t^2,...

does for a specific value of t. If that doesn't work then you have narrowed down your problem.

 

[Kortirion]

Hello and thanks for the reply.
I know what ListPlot does in that sense, however I thought it was worth a try since it did work to visualize an explicit functions amplitude like I wanted. Only now it failed with using something I've got as a solution. Bleh.

I've changed some stuff now to accommodate nonliterary in my system, so it's NDSolve now. From this I receive nice solutions, but I'd still like to visualize them simultaneously spaced equally on a line. These will look like dots moving up and down as I vary the parameter t on each "site". Get the picture?
I'm no pro at Mathematica, so do you know of any way to realize this? As I looked at it the Manipulate function and it looks like the best bet as I'd like to be able to vary t forth and back.

 

[Bill Simpson]

I'm sorry, but I don't get the picture.

Are you possibly trying to accomplish something like

Manipulate[
GraphicsRow[{
Plot[someCompletePlotDependingOnt],
Plot[someOtherCompletePlotDependingOnt],
Plot[yetAnotherCompletePlotDependingOnt],
Plot[etcCompletePlotDependingOnt]
}],
restOfMainpulateArgumentsIncludingt
]

http://reference.wolfram.com/mathematica/ref/GraphicsRow.html

 

[Kortirion]

Hey again. And no, that's not quite what I'd like. And ok, if you don't get my picture just run this and see

Manipulate[
ListPlot[{0.02 t^2, 0.4 t, 17 Sin[t], 0.4 t, 0.02 t^2},
PlotRange -> 30, Filling -> filling], {t, 0,
35}, {filling, {None, Axis, Bottom, Top}}]

It views the plot as one-dimensional, having those dots racing up and down. Maybe there's some better option to this than using ListPlot and the rest, but I don't know of any.. Thank you for your time trying to help, much appreciated.

 

[Kortirion]

Hello. Just reporting in that I solved this issue by using the "Block" command

Manipulate[
ListLinePlot[
Table[Block[{t = k}, Abs[Subscript[y, i][t] /. solution[[1]]]^2], {i, 50, 151}],
PlotRange -> {0, 0.7}, Filling -> Axis], {k, 0, 1100}]

With this it, as I wanted, actually took forth the value of my solution and did not treat it as an "object".