{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework 03a - Laplace Transforms Table

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

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

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

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

View Full Document
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)
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( " t ) + 2 # e-bt sin( t) \$ % & ’ ( ) 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

{[ snackBarMessage ]}

### Page1 / 3

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

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

View Full Document
Ask a homework question - tutors are online