The amplitude, period, frequency and angular frequency of y=6sin(3t) is

1 2 3 4 5 6

0% 0% 0%0%0%0%

3

1,

3

1,3,6

1.

3,2

3,

3

2,6

2.

3

2,

3

2,

2

3,6

3.

3,3

2,

2

3,6

4.

None of these5.

Don’t know6.

The amplitude, period, frequency and

angular frequency of is

1 2 3 4 5

0% 0% 0%0%0%

4cos2

ty

4,8

1,8,2

1.

4

1,

2,

2,2

2.

4

1,

8

1,8,2

3.

None of these4.

Don’t know5.

Find the period of .

.5 2

0% 0%0%0%

tttf 2sin2

1cos)(

1. 0.5

2. 2

3. π

4. 4π

What is meant by the amplitude of a function?

1 2 3 4

0% 0%0%0%

1. Maximum displacement from x=0

2. Maximum displacement from y=0

3. Interval at which the function is repeated

4. None of these

Find , where n is an integer.

1 2 3 4

0% 0%0%0%

ntdt2sin

1. 0, n≠0 and 0, n=0.

2. 1, n≠0 and 0, n=0.

3. 0, n≠0 and 1, n=0.

4. 1, n≠0 and 1, n=0.

For any integers m, n, .

1 2 3

0% 0%0%

0cossin mtdtnt

1. True

2. False

3. Don’t know

For any integers m, n,

1 2 3

0% 0%0%

mn

mnmnmtdtnt

0,0coscos

1. True

2. False

3. Don’t know

Is the function

1 2 3 4

0% 0%0%0%

01

00

01

)(

x

x

x

tf

1. Even

2. Odd

3. Neither

4. Don’t know

Is the function

1 2 3 4

0% 0%0%0%

tetf )(

1. Even

2. Odd

3. Neither

4. Don’t know

Is the function

1 2 3 4

0% 0%0%0%

1)( ttf

1. Even

2. Odd

3. Neither

4. Don’t know

Is the function

Even

Odd

Neith

er

Don’t k

now

0% 0%0%0%

ntnt cossin

1. Even

2. Odd

3. Neither

4. Don’t know

Is the function

Even

Odd

Neith

er

Don’t k

now

0% 0%0%0%

tt 2cossin 2

1. Even

2. Odd

3. Neither

4. Don’t know

Is the function

Even

Odd

Neith

er

Don’t k

now

0% 0%0%0%

tttf 6sin)(

1. Even

2. Odd

3. Neither

4. Don’t know

Which of the following is true for odd functions?

0% 0% 0%0%0%

0na1.

0

2

0

cos)(2

1cos)(

1ntdttfntdttfan

2.

0nb3.

None of the above4.

Don’t know5.

If f(t) is an even function, which of the following are true?

f(t)s

innt=odd bn=0

f(t)c

osnt=even

None of t

hese ...

0% 0%0%0%

1. f(t)sinnt=odd

2. bn=0

3. f(t)cosnt=even

4. None of these are true

is known as the:

1 2 3 4

0% 0%0%0%

tA 2cos2

1. First harmonic

2. Second harmonic

3. Third harmonic

4. Don’t know

For the function ,

the Fourier series would contain a constant term.

1 2 3

0% 0%0%

0,0

0,3)(

t

ttf

1. True

2. False

3. Don’t know

For the square wave function

,

the Fourier series would contain a constant term.

1 2 3

0% 0%0%

0,1

0,1)(

t

ttf

1. True

2. False

3. Don’t know

Find the Fourier series for |t| on (-π,π).

0% 0% 0%0%0%

...5cos

5

13cos

3

1cos

4

2tttt

1.

...5cos

5

13cos

3

1cos

4

2tttt

2.

...5cos

25

13cos

9

1cos

4

2tttt

3.

...5cos

25

13cos

9

1cos

4

2tttt

4.

Don’t know5.

Obtain the Fourier series for this function.

1 2 3 4 5

0% 0% 0%0%0%

)()4(,022

202)( tftf

tt

tttf

...

2

5sin

25

1

2

3sin

9

1

2sin

81

2

ttt

1.

...

2cos

25

1

2cos

9

1

2cos

81

2

ttt

2.

...

2

5cos

25

1

2

3cos

9

1

2cos

81

2

ttt

3.

None of the above4.

Don’t know5.

Obtain the Fourier series of the 2π periodic function f(t)=t2, - π<t< π.

1 2 3 4 5

0% 0% 0%0%0%

ntn

n

n

coscos

43 0

2

2

1.

ntn

n

n

coscos

43

2

12

2

2.

ntn

n

n

coscos

43 1

2

2

3.

None of these4.

Don’t know5.

The value represents

1 2 3 4

0% 0%0%0%

20a

1. The average value of f(t) over one period

2. Half the average value of f(t) over one period

3. Neither of these

4. Don’t know

For the given function, find the value of an.

1 2 3 4

0% 0%0%0%

)()4(,20,

02,0)( tftf

tt

ttf

...5,3,1,4

...6,4,2,0

22n

n

nan

1.

...6,4,2,2

...5,3,1,0

22n

n

nan

2.

...5,3,1,2

...6,4,2,0

22n

n

nan

3.

Don’t know4.

For the given function, find the value of

0% 0% 0%0%0%0%

.2

0a

)()4(,20,

02,0)( tftf

tt

ttf

01.

12.

13.

24.

2

15.

Don’t know6.

For the given function, find the value of bn.

0% 0%0%0%

)()4(,20,

02,0)( tftf

tt

ttf

...5,3,1,2

...6,4,2,2

nn

nnbn

1.

...5,3,1,

2

...6,4,2,2

nn

nnbn

2.

...5,3,1,4

...6,4,2,4

nn

nnbn

3.

None of these4.

For the function , find the value of bn.

1 2 3 4 5 6

0% 0% 0%0%0%0%

)2,0(,)( txtf

2

1.

n

22.

03.

n

24.

25.

Don’t know6.

Find the value of bn for this function.

1 2 3 4 5

0% 0% 0%0%0%

)()4(,022

202)( tftf

tt

tttf

1. -1

2. 0

3. 1/n

4. ½

5. Don’t know

When ,

the Fourier coefficient a3 is equal to

1 2 3 4 5

0% 0% 0%0%0%

)()2(,23

2

012

)( tftft

t

tt

tf

29

8

1.

23

8

2.

03.

29

8

4.

Don’t know5.

When ,

the Fourier coefficient a2 is equal to

1 2 3 4 5

0% 0% 0%0%0%

)()2(,23

2

012

)( tftft

t

tt

tf

29

8

1.

29

8

2.

23

8

3.0

4.

Don’t know5.

When ,

find the value of b3.

1 2 3 4 5

0% 0% 0%0%0%

)()4(,20,

02,0)( tftf

tt

ttf

3

21.

3

22.

03.

3

24.

Don’t know5.

Extend the function f(t)=t, 0≤t ≤1 as a periodic odd function and calculate its

Fourier sine series.

1 2 3 4 5

0% 0% 0%0%0%

1

sincos2

n

tnn

1.

1

sincos2

n

tnn

2.

1

sincos2

n

ntn

3.

12

sincos2

n

tnn

4.

Don’t Know5.