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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
229Harmonic Oscillator
© 2010 Taylor & Francis Group, LLC
Energies are time-dependent, and our analysis is simplied if we focus on time-average values.
Now,
1
2
1
2
1
2
2
0
2
2
0
2
πω
ωδ
πω
ωδ
πω π
/
d
/
dsin( )cos ()
/
tt
tt
−=
−=
//ω
.
Thus, for an average over one period of oscillation, we have
T
mB
V
kB
==
22 2
44
ω
,
and
E
Bm k
mB
=
+
=
()
22
22
0
2
44
()ω
ωω
.
Let us now nd the frequency ω
k
at which T is a maximum:
d
d
T
k
ω
ωω=
= 0 (7.80)
from which we obtain
ω
k
= ω
0
. (7.81)
Thus, the kinetic energy resonance occurs at the natural frequency ω
0
of the system for an undamped
oscillator. Because the potential energy is proportional to the square of the amplitude, we expect
that the potential ...
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Publisher Resources

ISBN: 9781466569980