1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin oot u(t) b. e-acos at u(t) c. f³u(t)
1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin oot u(t) b. e-acos at u(t) c. f³u(t)
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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Question
![1.
Using the Laplace transform pairs of Table 2.1 and the
Laplace transform theorems of Table 2.2, derive the
Laplace transforms for the following time functions:
[Section: 2.2]
a. e-a sin cot u(t)
b. e" cos cot u(t)
c. t³u(t)
2. Assuming zero initial conditions, use classical methods to find solutions for the
following differential equations:
4.
a.
dx
dt
+ 5x = 2 cos 3t
d²x
b. +4
3. Repeat Problem 2, using Laplace transforms. Assume that the forcing functions
are zero prior to t = 0_.
+3
dx
dt
+ 2x = 2 sin 1
A system is described by the following differential
equation:
d'y
d³x
d1³
d²x dx
+4 +6
di
+ 8x
Find the expression for the transfer function of the
system, Y(s)/X(s).
Hint: All initial conditions are assumed to be zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F995b01c6-0baf-4a59-9e51-957b551c07e4%2F596dffcb-439a-4a0a-9afb-fc04f0e43ff7%2F85f40g2h_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Using the Laplace transform pairs of Table 2.1 and the
Laplace transform theorems of Table 2.2, derive the
Laplace transforms for the following time functions:
[Section: 2.2]
a. e-a sin cot u(t)
b. e" cos cot u(t)
c. t³u(t)
2. Assuming zero initial conditions, use classical methods to find solutions for the
following differential equations:
4.
a.
dx
dt
+ 5x = 2 cos 3t
d²x
b. +4
3. Repeat Problem 2, using Laplace transforms. Assume that the forcing functions
are zero prior to t = 0_.
+3
dx
dt
+ 2x = 2 sin 1
A system is described by the following differential
equation:
d'y
d³x
d1³
d²x dx
+4 +6
di
+ 8x
Find the expression for the transfer function of the
system, Y(s)/X(s).
Hint: All initial conditions are assumed to be zero.
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