Homework 03a - Laplace Transforms Table

Homework 03a - Laplace Transforms Table - 4 1 3! t 3 e-bt S...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No. 3a — LAPLACE TRANSFORMS TABLE Use the Table of Laplace Transforms given in the textbook (Table 3.1) to fill-in the blank cells on the right-hand column of the tables given below. Do note use integration tables . The notation S (t) = 0 t < 0 1 t ! 0 ! " # represents the unit step function. 1.0 Complete the entries of the table given below, where n is a non-negative integer. Time-Domain Function f(t) Laplace Transform L [ f(t) ] 1 ! (t) S (t) 2 S (t) 3 t S (t) 4 1 2! t 2 S (t) 5 1 3! t 3 S (t) 6 1 4! t 4 S (t) ! ! 7 1 n! t n S (t), n ! 0
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2.0 Complete the entries of the table given below, where b is a real number and n is a nonnegative integer. Time-Domain Function f(t) Laplace Transform L [ f(t) ] 1 e -bt S (t) 2 t e -bt S (t) 3 1 2! t 2 e -bt S (t)
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4 1 3! t 3 e-bt S (t) 5 1 4! t 4 e-bt S (t) ! ! 6 1 n! t n e-bt S (t), n ! (See next page for Problem 3) 3.0 Complete the entries of the table given below, where b, ! , and are real numbers. Time-Domain Function f(t) Laplace Transform L [ f(t) ] 1 sin( t) S (t) 2 cos( t) S (t) 3 2 e-bt cos( &quot; t ) + 2 # e-bt sin( t) $ % &amp; ( ) S (t) 4 (2 ) 2 + (2 ) 2 e-bt sin( t+ $ ) S (t) where = arctan Hint : See class notes. Note : The L [ f(t) ] should contain ! and ! , but should not contain ! . 5 2 cos( t ) + 2 sin( t) [ ] S (t) 6 (2 ) 2 + (2 ) 2 sin( t+ ) S (t) where = arctan Hint : See class notes. Note : The L [ f(t) ] should contain ! and ! , but should not contain ! ....
View Full Document

This note was uploaded on 07/14/2011 for the course ECH 4323 taught by Professor Crissale during the Spring '10 term at University of Florida.

Page1 / 3

Homework 03a - Laplace Transforms Table - 4 1 3! t 3 e-bt S...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online