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Unformatted text preview: 68. We use nT /2 to represent the integer number of halfperiods speciﬁed in the problem. Note that
T = 2π/ω . We use the calculusbased deﬁnition of an average of a function:
sin (ωt − φ)
2 avg =
= 1
nT /2
2
nT nT
2 nT
2 0 sin2 (ωt − φ) dt 0 1 − cos(2ωt − 2φ)
dt
2
nT =
= 2
2t
1
−
sin(2ωt − 2φ)
nT 2 4ω
0
1
1
−
sin(nωT − 2φ) + sin 2φ .
2 2nT ω Since nωT = nω (2π/ω ) = 2nπ , we have sin(nωT − 2φ) = sin(2nπ − 2φ) = − sin 2φ so [sin(nωT − 2φ) +
sin 2φ] = 0. Thus,
1
sin2 (ωt − φ) avg = .
2 ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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