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Phase Plot of Simple Harmonic Motion using Mathematica ??
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More options May 15 2012, 4:56 am
Newsgroups: comp.soft-sys.math.mathematica
From: Rahul Chakraborty <rahul.6s...@gmail.com>
Date: Tue, 15 May 2012 08:56:13 +0000 (UTC)
Local: Tues, May 15 2012 4:56 am
Subject: Phase Plot of Simple Harmonic Motion using Mathematica ??
Hi all,

Plz check my code below for Phase plot of Simple Harmonic motion. The output should be a circle with x along X-axis and dxdt along y-axis.

I'm not getting the output. kindly let me know where i'm wrong.

Clear[k, m];
k = 1;
m = 3;
solution =
NDSolve[{x''[t] + k/m x[t] == 0, x[0] == 5, x'[0] == 0},
x, {t, 0, 250}, MaxSteps \[RightArrow] 50000,
WorkingPrecision \[RightArrow] 25]
ParametricPlot[Evaluate[{x[t], x'[t]} /. solution], {t, 0, 100},
PlotRange \[RightArrow] All,
AxesLabel -> {"x", "\!\(\*OverscriptBox[\(x\), \(.\)]\)"}]

Following are the errors:

1)NDSolve::dvlen: The function x[t] does not have the same number of arguments as independent variables (3). >>

2)ReplaceAll::reps: {NDSolve[{x[t]/3+(x^\[Prime]\[Prime])[t]==0,x[0]==5,(x^\[Prime])[0]==0},x,{ t,0,250},MaxSteps\[RightArrow]50000,WorkingPrecision\[RightArrow]25]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>

3)ParametricPlot::pllim: Range specification PlotRange\[RightArrow]All is not of the form {x, xmin, xmax}. >>

Regards,

rc

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More options May 16 2012, 4:26 am
Newsgroups: comp.soft-sys.math.mathematica
From: "Nasser M. Abbasi" <n...@12000.org>
Date: Wed, 16 May 2012 08:26:23 +0000 (UTC)
Local: Wed, May 16 2012 4:26 am
Subject: Re: Phase Plot of Simple Harmonic Motion using Mathematica ??
On 5/15/2012 3:56 AM, Rahul Chakraborty wrote:

This works for me. Just changed your \[RightArrow] with normal
ascii ->

NDSolve[{x''[t] + (k/m)*x[t] == 0, x[0] == 5,
x'[0] == 0}, x, {t, 0, 250}, MaxSteps -> 50000,
WorkingPrecision -> 25]

--Nasser

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More options May 16 2012, 4:23 am
Newsgroups: comp.soft-sys.math.mathematica
From: DC <b.gatessu...@gmail.com>
Date: Wed, 16 May 2012 08:23:19 +0000 (UTC)
Local: Wed, May 16 2012 4:23 am
Subject: Re: Phase Plot of Simple Harmonic Motion using Mathematica ??
I would change the definition of solution so it's a simple function of t, then you'd take its derivative/do the plot in the usual way.

solution[t_] =
NDSolve[{x''[t] + k/m x[t] == 0, x[0] == 5, x'[0] == 0},
x[t], {t, 0, 250}][[1, 1, 2]]
ParametricPlot[{solution[t], solution'[t]}, {t, 0, 100}]

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More options May 16 2012, 4:24 am
Newsgroups: comp.soft-sys.math.mathematica
From: Bob Hanlon <hanlonr...@gmail.com>
Date: Wed, 16 May 2012 08:24:20 +0000 (UTC)
Local: Wed, May 16 2012 4:24 am
Subject: Re: Phase Plot of Simple Harmonic Motion using Mathematica ??
When I copied and pasted your input I had the same error. However,
after I manually re-entered the line defining solution all worked
well. You must have some invisible character in your input.

Bob Hanlon

On Tue, May 15, 2012 at 4:54 AM, Rahul Chakraborty

<rahul.6s...@gmail.com> wrote:
> Hi all,

>  Plz check my code below for Phase plot of Simple Harmonic motion. The =

output should be a circle with x along X-axis and dxdt along y-axis.

ments as independent variables (3). >>

> 2)ReplaceAll::reps: {NDSolve[{x[t]/3+(x^\[Prime]\[Prime])[t]==0,x[0]=

==5,(x^\[Prime])[0]==0},x,{t,0,250},MaxSteps\[RightArrow]50000,Work=
ingPrecision\[RightArrow]25]} is neither a list of replacement rules nor a =
valid dispatch table, and so cannot be used for replacing. >>

> 3)ParametricPlot::pllim: Range specification PlotRange\[RightArrow]All is=

not of the form {x, xmin, xmax}. >>

> Regards,

> rc

--
Bob Hanlon

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More options May 16 2012, 4:25 am
Newsgroups: comp.soft-sys.math.mathematica
From: Christoph Lhotka <christoph.lho...@fundp.ac.be>
Date: Wed, 16 May 2012 08:25:22 +0000 (UTC)
Local: Wed, May 16 2012 4:25 am
Subject: Re: Phase Plot of Simple Harmonic Motion using Mathematica ??
Dear Rahul,

replace in your expression \[RightArrow] by \[Rule] (delete the arrows
and retype them properly).

If you look on the documentation for \[RightArrow]
you will find that it has no built-in meaning and that it can be entered
as [ESC]_->[ESC], where _ stands for an extra space, while \[Rule] is
entered as [ESC]->[ESC] only.

In the email text it is easy to see the difference between \[RightArrow]
and \[Rule], to
see the difference in your notebook just press Shift+Ctrl+E inside the
cell or use
Hold[expr]//FullForm to see the unevaluated fullform of the expression.

Best,

Christoph

Addendum: another issue is, that the error messages of the present
example are not really
related to the problem, does anyone know why?

On 05/15/2012 10:54 AM, Rahul Chakraborty wrote:

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More options May 17 2012, 4:07 am
Newsgroups: comp.soft-sys.math.mathematica
From: Alexei Boulbitch <Alexei.Boulbi...@iee.lu>
Date: Thu, 17 May 2012 08:07:51 +0000 (UTC)
Local: Thurs, May 17 2012 4:07 am
Subject: Re: Phase Plot of Simple Harmonic Motion using Mathematica ??
Hi all,

Plz check my code below for Phase plot of Simple Harmonic motion. The output should be a circle with x along X-axis and dxdt along y-axis.

I'm not getting the output. kindly let me know where i'm wrong.

Clear[k, m];
k = 1;
m = 3;
solution =
NDSolve[{x''[t] + k/m x[t] == 0, x[0] == 5, x'[0] == 0},
x, {t, 0, 250}, MaxSteps \[RightArrow] 50000,
WorkingPrecision \[RightArrow] 25]
ParametricPlot[Evaluate[{x[t], x'[t]} /. solution], {t, 0, 100},
PlotRange \[RightArrow] All,
AxesLabel -> {"x", "\!\(\*OverscriptBox[\(x\), \(.\)]\)"}]

Regards, Rc

Hi, Rahul,

Try this:

Clear[k, m];
k = 1;
m = 3;
solution =
NDSolve[{x''[t] + (k/m )*x[t] == 0, x[0] == 5, x'[0] == 0},
x, {t, 0, 250}] // Flatten
ParametricPlot[Evaluate[{x[t], x'[t]} /. solution], {t, 0, 100},
AxesLabel -> {"x", "x'"}, PlotRange -> All]

The main difference in the function Flatten that I apply to the solution. I t removes the extra parentheses. The latter have prevented you from getting solution.

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
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e-mail: alexei.boulbi...@iee.lu