Fourier and differential function

• To: mathgroup at smc.vnet.net
• Subject: [mg32804] Fourier and differential function
• From: Bostjan Ketis <bostjan_ketis at yahoo.com>
• Date: Tue, 12 Feb 2002 06:24:06 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I am a student of physics in Slovenia and I need a
discrete Fourier transformation of differential
function.
The differential function is describing a pole which
is moved out of balance for a large angle (by Pi/2 ),
and you change only angle.
I have ploted the graph of differencial function
(x-time, y-amplitude) and now I woude like to Plot a
diskrete Fourier transformation of that function.
I need a time on x-axsis. I know that the big signal
will be shown at t0(with my data is 3,66 s) and
smoller signals will bi shown at his n x to, n
=1,2,3,... The signals will show depending on the
angle.
Here is the differential function:

g = 9.81
r = 10
f1 = - x'[t] + y[t]
f2 = - y'[t] - ((3g)/r)Sin[x[t]]
initial = {x[0] == 3.14159265*(1/2), y[0] == 0}
eq1 = {f1 == 0, f2 == 0}
eq2 = Join[eq1, initial]
ndsol2 = NDSolve [eq2, {x[t], y[t]}, {t, 0, 100},
MaxSteps -> 100000][[1]]
x1[t] = x[t] //. ndsol2;
y1[t] = y[t] //. ndsol2;
Plot[x1[t], {t, 0, 20}, PlotRange -> All, AxesLabel ->
{t, x},
ImageSize -> {600, 500},
TextStyle -> {FontFamily -> Times, FontSize -> 20},
PlotPoints -> 6000]

I hope that you can help me and to hear soon from you.

Bostjan

P.S.: I hope that you understand my problem, because I
don't speak english very well. If you didn't understand
something please send me a e-mail back.

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```

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