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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
224 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Putting this into Equation 7.58 yields
At
Ft
m
e
it
()
()
=
−ω
0
. (7.61)
Integration gives the solution of Equation 7.58:
ye
Ft
m
ety
it it
t
=
+
ωω
00
0
0
()
()d
(7.62)
where y(0) is the constant of integration, the value of y at the time t = 0. Equation 7.62 is the required
general solution of a rst-order differential equation, Equation 7.58. From Equation 7.61, we see that
the function x(t) is given by the imaginary part of Equation 7.62, divided by ω
0
:
xt
yt
()
Im
()
=
ω
0
. (7.63)
Force F(t) in Equation 7.62 or 7.63 must be written in real form.
The energy of the system cannot be conserved as the sy ...
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Publisher Resources

ISBN: 9781466569980