The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5....
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Transcript of The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5....
![Page 1: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/1.jpg)
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.
![Page 2: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/2.jpg)
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.
![Page 3: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/3.jpg)
Find the period of .
.5 2
0% 0%0%0%
tttf 2sin2
1cos)(
1. 0.5
2. 2
3. π
4. 4π
![Page 4: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/4.jpg)
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
![Page 5: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/5.jpg)
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.
![Page 6: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/6.jpg)
For any integers m, n, .
1 2 3
0% 0%0%
0cossin mtdtnt
1. True
2. False
3. Don’t know
![Page 7: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/7.jpg)
For any integers m, n,
1 2 3
0% 0%0%
mn
mnmnmtdtnt
0,0coscos
1. True
2. False
3. Don’t know
![Page 8: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/8.jpg)
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
![Page 9: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/9.jpg)
Is the function
1 2 3 4
0% 0%0%0%
tetf )(
1. Even
2. Odd
3. Neither
4. Don’t know
![Page 10: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/10.jpg)
Is the function
1 2 3 4
0% 0%0%0%
1)( ttf
1. Even
2. Odd
3. Neither
4. Don’t know
![Page 11: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/11.jpg)
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
![Page 12: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/12.jpg)
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
![Page 13: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/13.jpg)
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
![Page 14: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/14.jpg)
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.
![Page 15: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/15.jpg)
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
![Page 16: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/16.jpg)
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
![Page 17: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/17.jpg)
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
![Page 18: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/18.jpg)
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
![Page 19: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/19.jpg)
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.
![Page 20: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/20.jpg)
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.
![Page 21: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/21.jpg)
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.
![Page 22: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/22.jpg)
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
![Page 23: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/23.jpg)
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.
![Page 24: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/24.jpg)
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.
![Page 25: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/25.jpg)
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.
![Page 26: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/26.jpg)
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.
![Page 27: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/27.jpg)
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
![Page 28: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/28.jpg)
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.
![Page 29: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/29.jpg)
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.
![Page 30: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/30.jpg)
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.
![Page 31: The amplitude, period, frequency and angular frequency of y=6sin(3t) is 1. 2. 3. 4. None of these 5. Don’t know 6.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c745503460f94927b3a/html5/thumbnails/31.jpg)
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.