This preview shows page 1. Sign up to view the full content.
Chapter 4
Thus (4.9) becomes
(
θ
0
)
2
2
−
cos
θ
=1
.
In particular, at the initial moment,
t
=0
,
[
θ
0
(0)]
2
2
−
cos[
θ
(0)] = 1
.
Since
θ
(0) = 0, we get
[
θ
0
(0)]
2
2
−
cos 0 = 1
⇒
[
θ
0
(0)]
2
=4
⇒
θ
0
(0) = 2
or
θ
0
(0) =
−
2
.
11.
The “damping coeﬃcient” in the Rayleigh equation is
b
=(
y
0
)
2
−
1. Thus, for low velocities
y
0
,w
ehav
e
b<
0, and
b>
0 for high velocities. Therefore, the low velocities are boosted,
while high velocities are slowed, and so one should expect a limit cycle.
13.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

Click to edit the document details