       Re: manipulate time

• To: mathgroup at smc.vnet.net
• Subject: [mg114771] Re: manipulate time
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Thu, 16 Dec 2010 05:50:47 -0500 (EST)

```manel zerelli wrote:

> i want to solve two differential equations in which a parameter "r"
> vary in an intervall. for that i want to see the effect of this
> variation at each time.i want to manipulate time and for each instant
> i scan all the interval of variation of parameter "r".
> i tried this:
>
> Manipulate[
> For[r = 1, r < 4, r++,
> sol = DSolve[{\[Theta]'[t] == k i[t],
> i'[t] == -k \[Theta][t] - r i[t] + 10,
> i == 0, \[Theta] == 0}, {i, \[Theta]}, t];
> ParametricPlot[Evaluate[{i[t], \[Theta][t]} /. sol], {t, 0, n},
> PlotRange -> {{-10, 10}, {-1, 15}}]], {n, 0, 7}]
>
> and i tried tu use two for loop
>
> For [t = 0.1, t < 7, t++,
> For[r = 1, r < 3, r++,
> sol = DSolve[{\[Theta]'[t] == k i[t],
> i'[t] == -k \[Theta][t] - r i[t] + 10,
> i == 0, \[Theta] == 0}, {i, \[Theta]}, t];
> ParametricPlot[Evaluate[{i[t], \[Theta][t]} /. sol], {t, 0.1, 7},
> PlotRange -> {{-10, 10}, {-1, 15}}]]]
>
> i am a new user of mathematica so i am sorry for the syntax error!
> can you help me o solve this problem
>

You have a k in your differential equation and therefore you can't plot
it without giving it a numeric value.

Try something like this:

sol = DSolve[{\[Theta]'[t] == k i[t],
i'[t] == -k \[Theta][t] - r i[t] + 10,
i == 0, \[Theta] == 0}, {i[t], \[Theta][t]}, t]

{fi[t_, r_, k_], f\[Theta][t_, r_, k_]} = {i[t], \[Theta][t]} /.
sol[]

Manipulate[
ParametricPlot[{fi[t, r, k], f\[Theta][t, r, k]}, {t, 0, 7},
PlotRange -> {{-10, 10}, {-1, 11}}],
{{k, 1}, 0.01, 20, Appearance -> "Labeled"},
{r, {1, 2, 3}}]

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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