       Re: Non-Linear pendulum

• To: mathgroup at smc.vnet.net
• Subject: [mg104938] Re: Non-Linear pendulum
• From: dh <dh at metrohm.com>
• Date: Fri, 13 Nov 2009 05:58:39 -0500 (EST)
• References: <hdgr31\$jbl\$1@smc.vnet.net>

```
Allamarein wrote:

> I'm getting to know Mathematica. I want to compile a code to see the

> non-linear pendulum behavior.

>

> pendulum= {Line[{{0, 0}, {0, -1}}], Circle[{0, -1.3}, 0.3]};

> l = 20;

> g = 9.81;

> s = NDSolve[

>    { \[Theta]''[t] == -g /l Sin[\[Theta][t]],

>     \[Theta] == Pi/2,

>     \[Theta]' == 0}, \[Theta],

>    {t, 0, 30}];

> Animate[

>  Graphics[Rotate[pendulum, \[Theta[]t], {0, 0}],

>   PlotRange -> {{-2, 2}, {0, -2}}],

>  {t, 0, 30}, AnimationRunning -> False]

>

> This code doesn't work. I realized my error is in Rotate argument. If

> I change this line with:

>

> Graphics[Rotate[pendulum, Sin[t], {0, 0}]

>

> code runs, but it's not the result (obviously).

> How can I correct my code, to see the pendulum oscillates with \[Theta]

> [t] law?

>

Hi Allamarein,

you have to treat the output of NDSolve correctly:

s = \[Theta] /.

NDSolve[{\[Theta]''[t] == -g/l Sin[\[Theta][t]], \[Theta] ==

Pi/2, \[Theta]' == 0}, \[Theta], {t, 0, 30}][];

Animate[Graphics[Rotate[pendulum, s[t], {0, 0}],

PlotRange -> {{-2, 2}, {0.5, -2}}], {t, 0, 30},

AnimationRunning -> True]

Daniel

```

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