0 ≤t≤1 t> 1 i) Find Laplace of f(t) using the definition of Laplace transform. - a) Given that f(t) = {(t−1)² > ii) Express f(t) in terms of unit step functions and hence, find £{f(t)}.
0 ≤t≤1 t> 1 i) Find Laplace of f(t) using the definition of Laplace transform. - a) Given that f(t) = {(t−1)² > ii) Express f(t) in terms of unit step functions and hence, find £{f(t)}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Help me solve this. i've provided appendix of equations if needed.
![Function
a (constant)
f
t"
sin at
cos at
sinh at
cosh at
eat f(t)
f(t-a)u(t-a)
t" f(t)
f(n) (t)
f(u) du
f(u)g(t-u) du
Trigonometric Identities:
APPENDIX
TABLE OF LAPLACE TRANSFORMS
Laplace Transforms
a
S
1
s-a
n!
50+1
a
s² + a²
S
+ a
2
a
s²-a²
S
2
s² - a²
2
F(s-a)
e-as F(s)
(-1)"F(")(s)
s"F(s)-sn-1f(0)-sn-2f (¹) (0) --
F(s)
S
F(s) G(s)
2sinAcosB = sin (A + B) + sin (A - B)
2cosAcosB = cos (A - B) + cos (A + B)
2sinAsinB = cos (A-B)- cos (A + B)
-f(n-1) (0)
sin 2A = 2 sin A cos A
cos 2A = cos²A - sin³A = 2 cos²A-1 = 1-2 sin²A
sin (A + B) = sin A cos B ± cos A sin B
sin A sin B
cos (A + B) = cos A cos B
cosh?A – sinh?A = 1
sinh (A + B) = sinh A cosh B + cosh A sinh B
cosh (A + B) = cosh A cosh B+ sinh A sinh B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83b03dd8-9c4e-4cbb-afac-50fcd26752ac%2Fbb1b9315-6a7c-4538-b314-61d3177bd830%2Fgq6amsq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Function
a (constant)
f
t"
sin at
cos at
sinh at
cosh at
eat f(t)
f(t-a)u(t-a)
t" f(t)
f(n) (t)
f(u) du
f(u)g(t-u) du
Trigonometric Identities:
APPENDIX
TABLE OF LAPLACE TRANSFORMS
Laplace Transforms
a
S
1
s-a
n!
50+1
a
s² + a²
S
+ a
2
a
s²-a²
S
2
s² - a²
2
F(s-a)
e-as F(s)
(-1)"F(")(s)
s"F(s)-sn-1f(0)-sn-2f (¹) (0) --
F(s)
S
F(s) G(s)
2sinAcosB = sin (A + B) + sin (A - B)
2cosAcosB = cos (A - B) + cos (A + B)
2sinAsinB = cos (A-B)- cos (A + B)
-f(n-1) (0)
sin 2A = 2 sin A cos A
cos 2A = cos²A - sin³A = 2 cos²A-1 = 1-2 sin²A
sin (A + B) = sin A cos B ± cos A sin B
sin A sin B
cos (A + B) = cos A cos B
cosh?A – sinh?A = 1
sinh (A + B) = sinh A cosh B + cosh A sinh B
cosh (A + B) = cosh A cosh B+ sinh A sinh B
![- 1)²
e³t
0 ≤ t ≤1
t> 1
i) Find Laplace of f(t) using the definition of Laplace transform.
a) Given that f(t) = {(t
>
ii) Express f(t) in terms of unit step functions and hence, find £{f(t)}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83b03dd8-9c4e-4cbb-afac-50fcd26752ac%2Fbb1b9315-6a7c-4538-b314-61d3177bd830%2Fnd3jcf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:- 1)²
e³t
0 ≤ t ≤1
t> 1
i) Find Laplace of f(t) using the definition of Laplace transform.
a) Given that f(t) = {(t
>
ii) Express f(t) in terms of unit step functions and hence, find £{f(t)}.
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