Solution: -T/20 u=t F(w) = = 10 Integrating by parts with; du = dt and 2 20 T CT/2 -icot F(0) = f(t) e ¹³ dt = [7727²7 ² -te -T/2 e f(t) 23/10/20 -iwT/2 2. T :{- T-iw -1 T/2 le-toot -iw COS -iw +eT/2 77/2 @T 2 J-T/2 + 2i @² + - t -2i e -iw.iw -2i e -icot sin- dv = e -toT/2 ωT f(t)= 77/2 -ioot dt 2i @ f(t)= = -iot dt -T/2 } +elT/2 1-(-1) T 1---²-2 COS @T 2 4i 2 Tw² = -iot -io @T 2 sin-
Solution: -T/20 u=t F(w) = = 10 Integrating by parts with; du = dt and 2 20 T CT/2 -icot F(0) = f(t) e ¹³ dt = [7727²7 ² -te -T/2 e f(t) 23/10/20 -iwT/2 2. T :{- T-iw -1 T/2 le-toot -iw COS -iw +eT/2 77/2 @T 2 J-T/2 + 2i @² + - t -2i e -iw.iw -2i e -icot sin- dv = e -toT/2 ωT f(t)= 77/2 -ioot dt 2i @ f(t)= = -iot dt -T/2 } +elT/2 1-(-1) T 1---²-2 COS @T 2 4i 2 Tw² = -iot -io @T 2 sin-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
I want a detailed solution
![Solution:
F(w) =
u=t
-T/2 O
=
10
2
F(w)= {]
T
27/₁1/²0
Integrating by parts with;
du = dt
and
2
- ²/1
=
f(t)
f(t)
= [ f(t)e-¹³ dt = |
е
T
T-iw
-1
T/2
-iot
te
- iw
-iw
77/2
J-T/2
-iwT/2
+eT/2
e
+
+
t
-2i
@T 2i
COS @²
2
T/2 2
e-icot
-iw.iw
-2i e
sin-
-T/2T
dv = e
-i@T/2
oᎢ .
2
f(t)=
-te
-}=
7/2
-iot
-T/2
+e"
@²
2i
-iont dt
f(t)=
=
dt
}
iwT/2
1-(-1)
T
T
1-(-5)
2
2
COS
@T
2
2/₁
-iwt
-io
4i ωT
sin-
Tw²
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94458cf2-014b-466a-bada-fa68de68f3b9%2F29e2cf38-6d62-488a-974a-0e4cb968f47e%2F4vhpqar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solution:
F(w) =
u=t
-T/2 O
=
10
2
F(w)= {]
T
27/₁1/²0
Integrating by parts with;
du = dt
and
2
- ²/1
=
f(t)
f(t)
= [ f(t)e-¹³ dt = |
е
T
T-iw
-1
T/2
-iot
te
- iw
-iw
77/2
J-T/2
-iwT/2
+eT/2
e
+
+
t
-2i
@T 2i
COS @²
2
T/2 2
e-icot
-iw.iw
-2i e
sin-
-T/2T
dv = e
-i@T/2
oᎢ .
2
f(t)=
-te
-}=
7/2
-iot
-T/2
+e"
@²
2i
-iont dt
f(t)=
=
dt
}
iwT/2
1-(-1)
T
T
1-(-5)
2
2
COS
@T
2
2/₁
-iwt
-io
4i ωT
sin-
Tw²
2
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