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Phase Plot of Simple Harmonic Motion using Mathematica ??
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Rahul Chakraborty
May 15, 2012, 4:56:13 AM5/15/12
to
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
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
Nasser M. Abbasi
May 16, 2012, 4:26:23 AM5/16/12
to
On 5/15/2012 3:56 AM, Rahul Chakraborty 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.
>
> 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]
>
>
> Following are the errors:
> 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]
>
>
>
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
DC
May 16, 2012, 4:23:19 AM5/16/12
to
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_] =
ParametricPlot[{solution[t], solution'[t]}, {t, 0, 100}]
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}]
Bob Hanlon
May 16, 2012, 4:24:20 AM5/16/12
to
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
> Plz check my code below for Phase plot of Simple Harmonic motion. The =
ingPrecision\[RightArrow]25]} is neither a list of replacement rules nor a =
Bob Hanlon
after I manually re-entered the line defining solution all worked
well. You must have some invisible character in your input.
Bob Hanlon
> 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 =
>
> I'm not getting the output. kindly let me know where i'm wrong.
>
> Clear[k, m];
> k = 1;
> m = 3;
> NDSolve[{x''[t] + k/m x[t] == 0, x[0] == 5, x'[0] == 0},
> x, {t, 0, 250}, MaxSteps \[RightArrow] 50000,
> WorkingPrecision \[RightArrow] 25]
> 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 argu=
> PlotRange \[RightArrow] All,
> AxesLabel -> {"x", "\!\(\*OverscriptBox[\(x\), \(.\)]\)"}]
>
>
> Following are the errors:
>
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=
>
> 2)ReplaceAll::reps: {NDSolve[{x[t]/3+(x^\[Prime]\[Prime])[t]==0,x[0]=
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
>
--
>
>
> Regards,
>
> rc
>
Bob Hanlon
Christoph Lhotka
May 16, 2012, 4:25:22 AM5/16/12
to
Dear Rahul,
this makes your code work:
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:
> 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.
>
> 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
>
this makes your code work:
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:
> Hi all,
>
>
> 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).>>
> 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:
>
>
> 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
>
Alexei Boulbitch
May 17, 2012, 4:07:51 AM5/17/12
to
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
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[\(x\), \(.\)]\)"}]
Hi, Rahul,
Try this:
Clear[k, m];
k = 1;
m = 3;
solution =
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
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.b...@iee.lu
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