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Related Pages
Related Symbols
NDEigensystem
Laplacian
Related Categories
Calculus
Physics
Modes of a Pentagon Drum
Compute and plot eigenmodes of a polygon drum
Example Notebook
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Solve for the eigenmodes of the Laplacian in a pentagon:
I
n
[
1
]
:
=
{
v
a
l
s
,
f
u
n
s
}
=
N
D
E
i
g
e
n
s
y
s
t
e
m
[
{
-
L
a
p
l
a
c
i
a
n
[
u
[
x
,
y
]
,
{
x
,
y
}
]
,
D
i
r
i
c
h
l
e
t
C
o
n
d
i
t
i
o
n
[
u
[
x
,
y
]
0
,
T
r
u
e
]
}
,
u
[
x
,
y
]
,
{
x
,
y
}
∈
R
e
g
u
l
a
r
P
o
l
y
g
o
n
[
5
]
,
6
]
O
u
t
[
1
]
=
Plot the computed eigenmodes:
I
n
[
2
]
:
=
T
a
b
l
e
[
P
l
o
t
3
D
[
f
u
n
s
〚
i
〛
,
{
x
,
y
}
∈
R
e
g
u
l
a
r
P
o
l
y
g
o
n
[
5
]
,
P
l
o
t
R
a
n
g
e
A
l
l
,
P
l
o
t
L
a
b
e
l
v
a
l
s
〚
i
〛
,
P
l
o
t
T
h
e
m
e
"
M
i
n
i
m
a
l
"
]
,
{
i
,
L
e
n
g
t
h
[
v
a
l
s
]
}
]
O
u
t
[
2
]
=
Related Symbols
NDEigensystem
Laplacian
Publisher Information
Contributed by:
Stephen Wolfram
