Mathematic Methods HW Solutions 36

Mathematic Methods HW Solutions 36 - Chapter 7 36 10.1 p(t)...

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Unformatted text preview: Chapter 7 36 10.1 p(t) = ∞ an cos 220nπt, a0 = 0 √ √ 2 2 an = nπ (sin nπ + sin 2nπ ) = nπ { 3, 0, 0, 0, − 3, 0, and repeat} 3 3 1 1 Relative intensities = 1 : 0 : 0 : 0 : 25 : 0 : 49 : 0 : 0 : 0 1 10.2 p(t) = ∞ bn sin 262nπt, where 1 2 bn = nπ (1 − cos nπ − 3 cos nπ + 3 cos 2nπ ) 3 3 2 = nπ {2, −3, 8, −3, 2, 0, and repeat} 9 4 Relative intensities = 4 : 9 : 64 : 16 : 25 : 0 4 9 10.3 p(t) = bn sin 220nπt 2 bn = − 5 cos nπ + 2 cos nπ ) = nπ {1, 10, 1, 0, and repeat} 2 1 1 1 1 Relative intensities = 1 : 25 : 9 : 0 : 25 : 25 : 49 : 0 : 81 : 1 9 2 nπ (3 10.4 V (t) = ∞ 200 1+ π 2 even n 2 cos 120nπt 1 − n2 Relative intensities = 0 : 1 : 0 : 10.5 I (t) = 5 1+ π ∞ 2 even n 1 25 3 : 0 : ( 35 )2 5 2 cos 120nπt + sin 120πt 2 1−n 2 10 Relative intensities = ( 5 )2 : ( 3π )2 : 0 : ( 32 )2 : 0 : ( 72 )2 2 π π = 6.25 : 1.13 : 0 : 0.045 : 0 : 0.008 10.6 V (t) = 50 − 400 π2 ∞ 1 odd n 1 cos 120nπt n2 Relative intensities = 1 : 0 : 14 3 14 5 :0: ∞ 20 (−1)n sin 120nπt π1 n 1 1 Relative intensities = 1 : 1 : 9 : 16 : 4 10.7 I (t) = − 5 20 − 10.8 I (t) = 2 π2 ∞ 1 odd n 1 25 10 1 cos 120nπt − n2 π ∞ 1 (−1)n sin 120nπt n 4 11 4 :: 1+ 2 2 π 49 9π = 1.4 : 0.25 : 0.12 : 0.06 : 0.04 Relative intensities = 10.9 V (t) = 400 π ∞ 1 odd n 1+ 200 π2 1 1 : 16 25 1 sin 120nπt n Relative intensities = 1 : 0 : 10.10 V (t) = 75 − : ∞ 1 odd n 1 9 :0: 1 25 100 1 cos 120nπt − n2 π ∞ 1 1 sin 120nπt n Relative intensities as in problem 10.8 11.5 π 2 /8 11.8 π 4 /96 11.6 π 4 /90 1 π2 − 11.9 16 2 11.7 π 2 /6 1+ 4 25π 2 ...
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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