13.4.1 By Fourier Series

13.4.1 By Fourier Series
In[1]:=
xsin@L_, omega_D = Integrate@x Sin@omega xD, 8x, 0, L<D
x2sin@L_, omega_D = Integrate@x ^ 2 Sin@omega xD, 8x, 0, L<D
- L omega Cos@L omegaD + Sin@L omegaD
Out[1]=
omega2
1
Out[2]=
omega3
In[3]:=
Out[3]=
I- 2 + I2 - L2 omega2 M Cos@L omegaD + 2 L omega Sin@L omegaDM
xsina@L_, j_D = Integrate@x Sin@omega xD, 8x, 0, L<D . 8omega ® j Pi  L<
x2sina@L_, j_D = Integrate@x ^ 2 Sin@omega xD, 8x, 0, L<D . 8omega ® j Pi  L<
L2 H- j Π Cos@j ΠD + Sin@j ΠDL
j2 Π2
Out[4]=
L3 H- 2 + H2 - j2 Π2 L Cos@j ΠD + 2 j Π Sin@j ΠDL
j3 Π3
In[5]:=
Integrate@x Cos@omega xD, 8x, 0, L<D
Integrate@x ^ 2 Cos@omega xD, 8x, 0, L<D
- 1 + Cos@L omegaD + L omega Sin@L omegaD
Out[5]=
omega2
1
Out[6]=
omega3
In[7]:=
Out[7]=
I2 L omega Cos@L omegaD + I- 2 + L2 omega2 M Sin@L omegaDM
Integrate@x Cos@omega xD, 8x, 0, L<D . 8omega ® j Pi  L<
Integrate@x ^ 2 Cos@omega xD, 8x, 0, L<D . 8omega ® j Pi  L<
L2 H- 1 + Cos@j ΠD + j Π Sin@j ΠDL
j2 Π2
Out[8]=
L3 H2 j Π Cos@j ΠD + H- 2 + j2 Π2 L Sin@j ΠDL
j3 Π3
In[9]:=
coeff@j_D = Hxsina@1, jD - x2sina@1, jDL  2
su@x_, t_, n_D := Sum@coeff@jD Cos@j Pi tD Sin@j Pi xD, 8j, 1, n<D
1
Out[9]=
- j Π Cos@j ΠD + Sin@j ΠD
-
2
j2 Π2
- 2 + H2 - j2 Π2 L Cos@j ΠD + 2 j Π Sin@j ΠD
j3 Π3
2
wavefs.nb
In[11]:=
Show@Plot@8su@x, 0, 1D, su@x, 0, 2D, su@x, 0, 3D, su@x, 0, 4D, su@x, 0, 5D<, 8x, 0, 1<D,
Plot@x H1 - xL  4, 8x, 0, 1<, PlotStyle ® RedDD
0.06
0.05
0.04
Out[11]=
0.03
0.02
0.01
0.2
In[12]:=
0.4
0.6
0.8
1.0
Plot3D@su@x, t, 3D, 8t, 0, 2<, 8x, 0, 1<, ViewPoint ® 81, 1, 1<D
0.05
0.00
Out[12]=
-0.05
0.0
0.0
0.5
0.5
1.0
1.5
1.0
2.0
wavefs.nb
In[18]:=
Animate@Plot@su@x, t, 3D, 8x, 0, 1<, PlotRange ® 8- .08, .08<D, 8t, 0, 10<D
t
0.05
Out[18]=
0.2
-0.05
0.4
0.6
0.8
1.0
3