(3.5) of the 3.1 Definition and Basic Properties 2. Use the definition of the Laplace transform to find the transform of r(t) = e-3t H(t-2). 3. Find the Laplace transform of r(t) = sin kt and x(t) = cos kt using the definitions 1 2i Check your answers in the table. 4. Find the Laplace transform of the hyperbolic functions r(t) = sinh kt and x(t) = cosh kt using the definitions sin kt = (eikt - e-ikt), cos kt = 2 (eikt + e-ikt). 145 1 1 sinh kt = (ekt - e-kt), cosh kt = 2 2 Check your answers in the table. (ekt + e-kt).
(3.5) of the 3.1 Definition and Basic Properties 2. Use the definition of the Laplace transform to find the transform of r(t) = e-3t H(t-2). 3. Find the Laplace transform of r(t) = sin kt and x(t) = cos kt using the definitions 1 2i Check your answers in the table. 4. Find the Laplace transform of the hyperbolic functions r(t) = sinh kt and x(t) = cosh kt using the definitions sin kt = (eikt - e-ikt), cos kt = 2 (eikt + e-ikt). 145 1 1 sinh kt = (ekt - e-kt), cosh kt = 2 2 Check your answers in the table. (ekt + e-kt).
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
Please do 4
![(3.5)
of the
Propert
w from th
3.1 Definition and Basic Properties
2. Use the definition of the Laplace transform to find the transform of r(t) =
e-3t H(t-2).
3. Find the Laplace transform of r(t)
definitions
-
sin kt and x(t)
1
sin kt = (eikt - e-ikt), cos kt =
2i
2
Check your answers in the table.
4. Find the Laplace transform of the hyperbolic functions r(t) = sinh kt and
x(t) = cosh kt using the definitions
a) 6+5e-2t + te³t.
b) tH(t-3).
c) cos 5t.
(eikt
1
1
sinh kt = (ekt - e-kt), cosh kt = (ekt + e-kt).
2
7. Use the preceding exercise to compute C[t² H (t-1)].
8. Find the Laplace transform of the following functions.
9. Find the inverse transform of the foll
cos kt using the
Check your answers in the table.
5. Derive the operational formulas (3.4) and (3.5) directly from the definition.
Hint: Change variables in the integrals.
6. Use the definition of Laplace transform to show that
L[f(t)H(ta)] = e as L[f(t + a)].
145
+ e-ikt).
uring functions
d) sin(2t + 7).
3e-t cosht..
f) H(tr) cos(t - π).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc10cce41-ef51-4545-a724-9736e236d3b7%2Fa9a45f1d-0cb1-411e-8550-3ff5efdf3eff%2Fbxtkwg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(3.5)
of the
Propert
w from th
3.1 Definition and Basic Properties
2. Use the definition of the Laplace transform to find the transform of r(t) =
e-3t H(t-2).
3. Find the Laplace transform of r(t)
definitions
-
sin kt and x(t)
1
sin kt = (eikt - e-ikt), cos kt =
2i
2
Check your answers in the table.
4. Find the Laplace transform of the hyperbolic functions r(t) = sinh kt and
x(t) = cosh kt using the definitions
a) 6+5e-2t + te³t.
b) tH(t-3).
c) cos 5t.
(eikt
1
1
sinh kt = (ekt - e-kt), cosh kt = (ekt + e-kt).
2
7. Use the preceding exercise to compute C[t² H (t-1)].
8. Find the Laplace transform of the following functions.
9. Find the inverse transform of the foll
cos kt using the
Check your answers in the table.
5. Derive the operational formulas (3.4) and (3.5) directly from the definition.
Hint: Change variables in the integrals.
6. Use the definition of Laplace transform to show that
L[f(t)H(ta)] = e as L[f(t + a)].
145
+ e-ikt).
uring functions
d) sin(2t + 7).
3e-t cosht..
f) H(tr) cos(t - π).
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