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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
204 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
KKtt
=
1
0
τ
τ
()d .
Because the motion of an oscillator is repetitive, the time average over one period is the same as
over many periods and is unique.
Now, for an oscillator whose motion obeys Equation 7.10, x = a sin(ω
0
t + θ
0
), and the period
τ=2πω
0
:
〈〉==
+
Tmxma
tt
11
2
1
22
2
0
0
22
2
00
0
2
0
τ
ω
ωθ
π
τ
πω
cos( )
/
d
//ω
0
.
Because the integral is extended over a complete period, it does not matter what the value of the
initial phase θ
0
is, and we may conveniently set θ
0
= 0. Using the fact that
ω
π
ω
π
πω π
0
2
0
0
2
2
0
2
2
1
2
1
2
0
co
sc
os
/
tt yd
∫∫
==
we nd
Tm
xm
a
==
11
2
1
4
2
0
0
22
τ
ω
τ
.
The potential energy is (again, θ
0
= 0)
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Publisher Resources

ISBN: 9781466569980