Note that we also have Laplace(g(t)U(t-a)}=eas (a) Find the Laplace transform of the piecewise defined function OB. f(t)=t for 03 OA O C. O D. df dt F(s) = OA sF(s)-f(0) 1 F(s) = 38 + 2 F(s) = F(S)=2 F(s) = S 1 5 + + S-1 1- -3s 3s 5 S-1 - 3e -3s (s-3)² S-4 OE. None of the given answers is correct 5e-3s (b) Find the inverse Laplace transform of the function -1 4 3s 4 s+2 (S-1)³ s²+1 (S-2)² +9 5e-3(s-1) + s-1 4 f(t)=-e2t+4e³1 - 3 cost + sin (3t) B. -te-2t+4e31 - 3 cost +2e⁹t sin (2t) O C. 4 f(t)= - e 2t +2t²e¹-3 cost + 3 Laplace{g(t + a)X(s) e²¹ sin (3t) OD. f(t)=-e²t +21²e-3 cost +2e-2¹ sin (3t) OE. None of the given answers is correct

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4please show written work part A and B
sF(s)-f(0)
Note that we also have Laplace(g(t)U(t-a)}=eas
(a) Find the Laplace transform of the piecewise defined function
f(t)=t for 0<t<3 and f(t)=5e for t>3
OA
OB.
O C.
O D.
df
dt
F(s) =
1
F(s) = 38 +
2
OA.
F(S)=2
F(s) =
F(s) =
1 5
+
S
1-
+
S-1
3s
-3s
5
8-1
-
3e
-3s
(s-3)²
S-4
OE. None of the given answers is correct
5e-3s
(b) Find the inverse Laplace transform of the function
-1
4
3s
4
s+2 (S-1)³ s²+1 (S-2)² +9
5e-3(s-1)
+
s-1
4
f(t)=-e2t+4e³1 - 3 cost +
sin (31)
B. -te-2t+4e³t-3 cost+2e⁹t sin(2t)
O C.
4
f(t)= e 2t +2t²e¹-3 cost +
3
e²¹ sin (3t)
Laplace(g(t + a)(s)
OD. f(t)=-e²t + 2t1²e-3 cost +2e-2¹ sin (3t)
OE. None of the given answers is correct
Transcribed Image Text:sF(s)-f(0) Note that we also have Laplace(g(t)U(t-a)}=eas (a) Find the Laplace transform of the piecewise defined function f(t)=t for 0<t<3 and f(t)=5e for t>3 OA OB. O C. O D. df dt F(s) = 1 F(s) = 38 + 2 OA. F(S)=2 F(s) = F(s) = 1 5 + S 1- + S-1 3s -3s 5 8-1 - 3e -3s (s-3)² S-4 OE. None of the given answers is correct 5e-3s (b) Find the inverse Laplace transform of the function -1 4 3s 4 s+2 (S-1)³ s²+1 (S-2)² +9 5e-3(s-1) + s-1 4 f(t)=-e2t+4e³1 - 3 cost + sin (31) B. -te-2t+4e³t-3 cost+2e⁹t sin(2t) O C. 4 f(t)= e 2t +2t²e¹-3 cost + 3 e²¹ sin (3t) Laplace(g(t + a)(s) OD. f(t)=-e²t + 2t1²e-3 cost +2e-2¹ sin (3t) OE. None of the given answers is correct
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