Skip to Main Content
Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
8.5. Consider a uniform string fixed at both ends. It has mass per unit length m, length L, and tension
T. A spring with stiffness k is attached to the string at x = L/2. Find the eigenfunctions and eigenvalues.
Solution: Let us divide the string into two segments. Let y
L
be the displacement for the segment to
the left of the spring and y
2
for the segment to the right of the spring. y
L
is defined between x
1
= 0 and
x
1
= L/2 and y
2
between x
2
= 0 and x
2
= L/2 as shown in Figure 31. The equations of motion are given by
L
k
m T
,
L
/2
x
1
Figure 31: String configuration
T
1
y

1
m¨y
1
= 0 for 0 < x
1
< L/2
T
2
y

2
m¨y
2
= 0 for 0 < x
2
< L/2.
For now, it is assumed that the tension ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Adaptive Learning Methods for Nonlinear System Modeling

Adaptive Learning Methods for Nonlinear System Modeling

Danilo Comminiello, Jose C. Principe
Mathematical Methods in Dynamical Systems

Mathematical Methods in Dynamical Systems

S. Chakraverty, Subrat Kumar Jena

Publisher Resources

ISBN: 9781439849897