21 o (z) = of the nth mode is cos for all n n² for odd n and 0 for even n n² for even n and 0 for odd n 2 for even n and 0 for odd n cos for odd n and 0 for even 2 a for all n 學 a for even n and 0 for odd n - all n

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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A string of length I and mass m fixed at both ends is struck by a mallet of width a about its center point. At
the moment of impact the displacement y(z, 0) = 0, but the velocity is given by
so
(0, -
o (z) =
%3D
lv, z-<
The energy of the nth mode is
Select one:
Am cos for all na
4my
sin for odd n and 0 for even n
sin for even n and 0 for odd n
2 naa
Ame sin a for even n and 0 for odd n
Am cos for odd n and 0 for even n
sin a for all n
Ame cos? na for even n and 0 for odd n
for all n
Transcribed Image Text:A string of length I and mass m fixed at both ends is struck by a mallet of width a about its center point. At the moment of impact the displacement y(z, 0) = 0, but the velocity is given by so (0, - o (z) = %3D lv, z-< The energy of the nth mode is Select one: Am cos for all na 4my sin for odd n and 0 for even n sin for even n and 0 for odd n 2 naa Ame sin a for even n and 0 for odd n Am cos for odd n and 0 for even n sin a for all n Ame cos? na for even n and 0 for odd n for all n
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