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Mathematic Methods HW Solutions 36

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

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Chapter 7 36 10.1 p ( t ) = summationdisplay 1 a n cos 220 nπt , a 0 = 0 a n = 2 (sin 3 + sin 2 3 ) = 2 { 3 , 0 , 0 , 0 , - 3 , 0, and repeat } Relative intensities = 1 : 0 : 0 : 0 : 1 25 : 0 : 1 49 : 0 : 0 : 0 10.2 p ( t ) = summationdisplay 1 b n sin 262 nπt , where b n = 2 (1 - cos 3 - 3 cos + 3 cos 2 3 ) = 2 { 2 , - 3 , 8 , - 3 , 2 , 0, and repeat } Relative intensities = 4 : 9 4 : 64 9 : 9 16 : 4 25 : 0 10.3 p ( t ) = summationdisplay b n sin 220 nπt b n = 2 (3 - 5 cos 2 + 2 cos ) = 2 { 1 , 10 , 1 , 0, and repeat } Relative intensities = 1 : 25 : 1 9 : 0 : 1 25 : 25 9 : 1 49 : 0 : 1 81 : 1 10.4 V ( t ) = 200 π bracketleftbigg 1 + summationdisplay 2 even n 2 1 - n 2 cos 120 nπt bracketrightbigg Relative intensities = 0 : 1 : 0 : 1 25 : 0 : ( 3 35 ) 2 10.5 I ( t ) = 5 π bracketleftbigg 1 + summationdisplay 2 even n 2 1 - n 2 cos 120 nπt bracketrightbigg + 5 2 sin 120 πt Relative intensities = ( 5 2 ) 2 : ( 10 3 π ) 2 : 0 : ( 2 3 π ) 2 : 0 : ( 2 7 π ) 2 = 6 . 25 : 1 . 13 : 0 : 0 . 045 : 0 : 0 . 008 10.6 V ( t ) = 50 - 400 π 2 summationdisplay 1 odd n 1 n 2 cos 120 nπt Relative intensities = 1 : 0 : ( 1 3 ) 4 : 0 : ( 1 5 ) 4 10.7 I ( t ) = - 20 π summationdisplay 1 ( - 1) n n sin 120 nπt Relative intensities = 1 :
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