f() = 314 + 1 Use the Laplace Transform properties table to convert this function into F(s). Lis(1) + 8(1)) = L{s()) + L1s(1)} %3D L{C f(t)) = CLs(1)} e{e^!s(1)}(s) = L{s())(s - A) LAf(1))(s) = s LIf(1))-f(0) L{f"(1)) (s) = s? L(f(i)} - Sf (0) - f'(0) L{sN(1)}(s) = sN LAS(1)) - SN -f (0) - sN - 2f (0) - sN - 3f"(0) - ... - N - '(0) e(Ns()(s) = (-1)" ((9ı1() (8)]
f() = 314 + 1 Use the Laplace Transform properties table to convert this function into F(s). Lis(1) + 8(1)) = L{s()) + L1s(1)} %3D L{C f(t)) = CLs(1)} e{e^!s(1)}(s) = L{s())(s - A) LAf(1))(s) = s LIf(1))-f(0) L{f"(1)) (s) = s? L(f(i)} - Sf (0) - f'(0) L{sN(1)}(s) = sN LAS(1)) - SN -f (0) - sN - 2f (0) - sN - 3f"(0) - ... - N - '(0) e(Ns()(s) = (-1)" ((9ı1() (8)]
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
q11
![Sometimes the function we need to find the Laplace Transform of is a combination of functions (aka: 2 or more functions added
together), a constant multiplied by a function, the derivative of a function, etc. so we have to use some additional rules in addition
to the rules used on the previous questions in order to find the Laplace Transform.
f(1) = 314 + 1
Use the Laplace Transform properties table to convert this function into F(s).
LAf(1) + 8(t)} = L{f(1)} + Z{ 8(1)}
L{C f(t)} = CLs(1)}
g{eA'f(1)}(s) = 21s() ) (s – A)
L{f (1))(s) = s L{f(t)} - f(0)
L{f"(1)} (s) = s2 L{f(1)} - Sf(0) - f"(0)
L{f"(1)}(s) = sN Lif(i)} - sN - !f(0) - sN - 2f (0) - sN -(0)
- fN - '(0)
....
d N
g{Ns()}(s) = (-1)" Fs) ()]
ds](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fced20a7a-5f6b-4ed8-baa5-7011ff618332%2F10bb1f5e-987e-469b-bc88-0fbf9a79adec%2Faeog2x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sometimes the function we need to find the Laplace Transform of is a combination of functions (aka: 2 or more functions added
together), a constant multiplied by a function, the derivative of a function, etc. so we have to use some additional rules in addition
to the rules used on the previous questions in order to find the Laplace Transform.
f(1) = 314 + 1
Use the Laplace Transform properties table to convert this function into F(s).
LAf(1) + 8(t)} = L{f(1)} + Z{ 8(1)}
L{C f(t)} = CLs(1)}
g{eA'f(1)}(s) = 21s() ) (s – A)
L{f (1))(s) = s L{f(t)} - f(0)
L{f"(1)} (s) = s2 L{f(1)} - Sf(0) - f"(0)
L{f"(1)}(s) = sN Lif(i)} - sN - !f(0) - sN - 2f (0) - sN -(0)
- fN - '(0)
....
d N
g{Ns()}(s) = (-1)" Fs) ()]
ds
Transcribed Image Text:® F(1) -
72
s4
12
1
(B)
F(s)
$5
S
72
©F(s)
24
F(s)
s4
© r(1) -
72
(E)
F(s)
O F(1) -
24
1
(F
S
25
G
F(s):
s5 + S
+
+
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