APPM 4/5350 Worksheet Week 1
Figure 1:
www.xkcd.com
1.
ODEs
(a)
Find a solution
θ
(
t
)
for:
m
¨
θ
=

g
sin(
θ
)
with small angle approximation
sin(
θ
)
≈
θ
, and initial conditions
θ
(0) = 0
,
˙
θ
(0) = 1
(b)
Obtain a general solution
y
(
t
)
(including arbitrary constants) for
y
0
+
βty
= 1
β
=
const
2.
Equilibrium Solution
Find the general equilibrium solution (including arbitrary constants) for:
∂
2
g
∂t
2
=
∂
2
g
∂x
2

αg,
α >
0
What does it mean to have an equilibrium solution and given
g
(
x,t
)
how would one ﬁnd
the equilibrium behavior if it exists.
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This note was uploaded on 10/24/2010 for the course APPM 4350 taught by Professor Ablowitz during the Fall '08 term at Colorado.
 Fall '08
 ABLOWITZ

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