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Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
162 Applied calculus of variations for engineers
then the first coefficient will be simply the y
m
amplitude:
c
1
= y
m
,
since
sin(
π
L
L
2
)=sin(
π
2
)=1.
Similar, but not identical, considerations may be applied for the coefficients
of the higher normal modes.
The natural frequencies depend on the physical conditions, such as the pre-
applied tension force distribution and the material characteristics embodied
in the unit weight ρ. Specifically, the higher the tension force F in the string,
the higher the frequency becomes. A very tight string vibrates very quickly
(with high frequency), while a very loose string vibrates slowly.
11.2 The elastic membrane
We now turn our ...
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Publisher Resources

ISBN: 9781482253597