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solution_quiz1

# solution_quiz1 - Problem(1(a Use phasors to simplify the...

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Unformatted text preview: Problem (1) (a). Use phasors to simplify the sum ) 4 . cos( ) 3 / 2 4 . cos( 2 ) 3 / 4 . cos( ] [ φ π π + = + + + = n A n n n x The values of A and φ are obtained as )] 3 2 sin( 2 ) 3 [sin( ) 3 2 cos( 2 ) 3 cos( 2 3 / 2 3 / π π π π π π φ + + + = + = j e e Ae j j j 761 . 1 6457 . 2 598 . 2 5 . ] 732 . 1 866 . [ 1 5 . j e j j = +- = + +- = Therefore ) 761 . 1 4 . cos( 6457 . 2 ] [ + = n n x (b) 5 , 24 , 2 12 5 3 , 16 , 2 8 3 2 2 1 1 = = = = = = r A n r n r n r n π π π π The period is the LCM of {16, 24}=48. Power: 625 . 1 2 / 25 . 2 / 1 1 ) 3 / 12 / 5 cos( 5 . * ) 8 / 3 cos( * 2 ) 3 / 12 / 5 cos( 5 . * 2 ) 8 / 3 cos( 2 ) 3 / 12 / 5 ( cos 25 . ) 8 / 3 ( cos 1 ( 48 1 | ) 3 / 12 / 5 cos( 5 . ) 8 / 3 cos( 1 | 48 1 | ] [ | 48 1 ) 2 2 47 2 47 2 47 2 = + + = + + + + + + + + = + + + = = ∑ ∑ ∑ = = = π π π π π π π π π π π π n n n n n n n n n x P n n n (c) ] 2 [ 5 . ] 1 [ ] [ 5 . ] 1 [ 2 ] 2 [ ] [- +--- + + + = n n n n n n z δ δ δ δ δ Since ] 1 [ ] [ ] [-- = n u n u n δ ] 2 [ 5 . ] 1 [ ] [ 5 . ] 1 [ 2 ] 2 [ ] [- +--- + + + = n n n n n n z δ δ δ δ δ ]) 3 [ ] 2 [ ( 5 . ]) 2 [ ] 1 [ ( ]) 1 [ ] [ ( 5 . ]) [ ] 1 [ ( 2 ] 1...
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solution_quiz1 - Problem(1(a Use phasors to simplify the...

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