8/12/2019 ODE E Assignment6

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ODE E6 - 1

ODE Chapter 6 EAssignment

Fourier Series Expansion of Trigonometric Functions

6-1 (ODE Sample Exam Q1) The Fourier coefficients of )4cos()4sin()(cos)( 2 xxxxf += are

.zeroesareandotheralland(E)

.zeroesareandotheralland2,2,2(D)

.zeroesareandotheralland2,2,2(C)

.zeroesareandotheralland,,(B)

.zeroesareandotheralland,,(A)

21

0

820

420

21

821

221

0

21

421

221

0

nn

nn

nn

nn

nn

baa

babaa

babaa

babaa

babaa

=

===

===

===

===

6-2 (ODE Sample Exam Q2) The Fourier coefficients of

)10cos(22)5(sin8)(412+= xxxf are

.zeroesareandotheralland2,6,0(E)

.zeroesareandotheralland2,6,4(D)

.zeroesareandotheralland2,6,4(C)

.zeroesareandotheralland8,,0(B)

.zeroesareandotheralland8,1,0(A)

10100

10100

10100

543

100

5100

nn

nn

nn

nn

nn

babaa

babaa

babaa

babaa

babaa

===

===

===

===

===

6-3 (Final Sep 2006 Q14) The function )(cos2: 2 xxf a is periodic with period 2.

Suppose that we express it as a Fourier series

=

++=

1

0 )sin()cos()(n

nn nxbnxaaxf .

Decide which of the following statements is TRUE.

.falseallare(D)and(C)(B),(A),(E)

1and1(D)

1and0(C)

0and1(B)0and0(A)

20

20

20

20

==

==

==

==

aa

aa

aaaa

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ODE E6 - 2

6-4 (Supplementary Final Sep 2006 Q14) The function )(sin2: 2 xxf a is periodic with

period 2.Suppose that we express it as a Fourier series

=

++=

1

0 )sin()cos()(n

nn nxbnxaaxf .

Decide which of the following statements is TRUE.

.falseallare(D)and(C)(B),(A),(E)

1and1(D)

1and0(C)

1and1(B)

1and0(A)

20

20

20

20

==

==

==

==

aa

aa

aa

aa

6-5 (Final Apr 2007 Q14) The function )(cos2: 2 xxf a is periodic with period 2.

Suppose that we express it as a Fourier series

=

++=

1

0 )sin()cos()(n

nn nxbnxaaxf .

Decide which of the following statements is TRUE.

.falseallare(D)and(C)(B),(A),(E)

1and1(D)

1and0(C)0and1(B)

0and0(A)

20

20

20

20

==

==

==

==

aa

aaaa

aa

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ODE E6 - 3

Fourier Series Expansion of Arbitrary Functions

6-6 (ODE Sample Exam Q3) The function 2: xxf a is periodic with period 2.Suppose

that we express it as a Fourier series

=

++=

1

0 )sin()cos()(n

nn nxbnxaaxf .

The Fourier coefficients 110 and, baa are, respectively :

.0and0,1(E)

.0and4,1(D)

.0and4,

3

1(C)

.0and4,3

(B)

.0and4,3

(A)

110

110

110

110

11

2

0

===

===

===

===

===

baa

baa

baa

baa

baa