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HW 4

This document provides problems related to using the Laplace transform to analyze signals and systems. It includes proving properties of the Laplace transform, taking the Laplace transform of various signals, and finding the inverse Laplace transform of functions.

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45 views1 page

HW 4

This document provides problems related to using the Laplace transform to analyze signals and systems. It includes proving properties of the Laplace transform, taking the Laplace transform of various signals, and finding the inverse Laplace transform of functions.

Uploaded by

foof faaf
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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EE 327 Signals and Systems 1

Homework 4

1. Use the definition of the Laplace transform to prove that


ω
L{sin (ωt )} =
s +ω2
2

2. Use the definition of the Laplace transform to prove that


{ }
a. L e − at f (t ) = F (s + a )
dF (s )
b. L{tf (t )} = −
ds

3. Find the Laplace transform of the following continuous-time signals.


a. x(t ) = 5
b. x(t ) = 5te −3t
c. x(t ) = 5e −3t cos(5t )u (t )

4. Find the following Laplace transforms. Assume all initial conditions are zero.
d 
a. L  t 2 e −3t 
 dt 
 d  
3

b. L   t 2 
 dt  
{
c. L 3t 3 (t − 1) + e −5t }
5. Find the inverse Laplace transform of
5s + 13
X (s ) = 2
s + 6s + 5

6. Find the inverse Laplace transform of


F (s ) = 2
1
( )(
s + 4 s2 − 4 )
7. Find the inverse Laplace transform of
G (s ) =
1
(s + 1)(s + 2)2

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