(b) f(t)=t-2 [Hint: write as a piecewise function!]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
How was part b simplified?
![●●●
Q6 Find Laplace transforms of the following functions:
Recall : L(u₂lt) + f(t-c)) = ²²³F(³)
e
cos 3t if 0 < t < 2
4 if 2 ≤ t
(a) f(t) =
You may find the identity cos(x + y):
= cos x cos y sinasiny useful.
f(t) =
cos 3t (1-4₂²t))
+ 4u₂(t)
= cos 3t - 4₂ lt) cos ( 3 (t-2) + 6) + 4u₁₂ (4)
Need £ (cos(3t+ 6)):
cos (3++6)= (cos6) cos 3€ - ({in 6) sin 3t
So £ (cos(3++6)) =
(c056) 5.
3 sinb
$²+9
s²+9
-25
F(x): ²3-09-22²¹ (2006) - 3646) + 46"
sin b
=
че
e
5219
$²+9/
$
(b) f(t) = |t2| [Hint: write as a piecewise function!]
(-(1-2) ost²2
f(t) =
| +-2
+22
= -(t-2) (1 − u₂lt)) + (+-2) u₂lt)
= 2-+ + 2(t-2) u₂ (t)
·25
F(s)= = - =—/20 + 2€ 2
5²
25,
6
inivimüüvišeðan vedenia chán névà vántážinininkvärmeväänänen kausiebeskin](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae98b63a-c1e0-40a0-8ef8-c296ebcafc68%2F368d21d3-97ec-4e03-89c3-60fc84fef65f%2Fxvbkmyp_processed.png&w=3840&q=75)
Transcribed Image Text:●●●
Q6 Find Laplace transforms of the following functions:
Recall : L(u₂lt) + f(t-c)) = ²²³F(³)
e
cos 3t if 0 < t < 2
4 if 2 ≤ t
(a) f(t) =
You may find the identity cos(x + y):
= cos x cos y sinasiny useful.
f(t) =
cos 3t (1-4₂²t))
+ 4u₂(t)
= cos 3t - 4₂ lt) cos ( 3 (t-2) + 6) + 4u₁₂ (4)
Need £ (cos(3t+ 6)):
cos (3++6)= (cos6) cos 3€ - ({in 6) sin 3t
So £ (cos(3++6)) =
(c056) 5.
3 sinb
$²+9
s²+9
-25
F(x): ²3-09-22²¹ (2006) - 3646) + 46"
sin b
=
че
e
5219
$²+9/
$
(b) f(t) = |t2| [Hint: write as a piecewise function!]
(-(1-2) ost²2
f(t) =
| +-2
+22
= -(t-2) (1 − u₂lt)) + (+-2) u₂lt)
= 2-+ + 2(t-2) u₂ (t)
·25
F(s)= = - =—/20 + 2€ 2
5²
25,
6
inivimüüvišeðan vedenia chán névà vántážinininkvärmeväänänen kausiebeskin
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