Multiplication by s et if 0 1 a(t) = { et if 0 1 show that the rule L[f(t)] = -fo + sF(s) holds for g but not for f. Why is it so? %3D
Multiplication by s et if 0 1 a(t) = { et if 0 1 show that the rule L[f(t)] = -fo + sF(s) holds for g but not for f. Why is it so? %3D
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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![if 0 <t <1
0 ift > 1
Multiplication by s
et if 0 <t < 1
e ift >1
3. Let f(t) = {e
and g(t) =
Find F(s) and G(s) and
show that the rule L[f (t)| = -fo + sF(s) holds for g but not for f. Why is it so?
4. Given f(t) :
S2t if 0 <t <1
It
find (a) F(s), (b) L[f (t)|. Does the rule
if t > 1,
L[f(t)] = -fo + sF(s) hold? Explain.
St² if 0 <t < 1
if t> 1,
%3D
5. Given f(t) ={,
find (a) F(s), (b) L[F(t)]. Does the rule
L[F(t)] = -fo – sfo + s²F(s) hold? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1cf9d96-4d1c-428b-b001-5ba8c0ac57d2%2F55ab8738-8d79-4bc8-8174-5ff8c7902f2c%2Fjh185nn_processed.png&w=3840&q=75)
Transcribed Image Text:if 0 <t <1
0 ift > 1
Multiplication by s
et if 0 <t < 1
e ift >1
3. Let f(t) = {e
and g(t) =
Find F(s) and G(s) and
show that the rule L[f (t)| = -fo + sF(s) holds for g but not for f. Why is it so?
4. Given f(t) :
S2t if 0 <t <1
It
find (a) F(s), (b) L[f (t)|. Does the rule
if t > 1,
L[f(t)] = -fo + sF(s) hold? Explain.
St² if 0 <t < 1
if t> 1,
%3D
5. Given f(t) ={,
find (a) F(s), (b) L[F(t)]. Does the rule
L[F(t)] = -fo – sfo + s²F(s) hold? Explain.
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