Homework 03a - Laplace Transforms Table

Homework 03a - Laplace Transforms Table - 3.0 Complete the...

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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 ³ 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 δ (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) M M 7 1 n! t n S(t), n ≥ 0
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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) 4 1 3! t 3 e -bt S(t) 5 1 4! t 4 e -bt S(t) M M 6 1 n! t n e -bt S(t), n ≥ 0 (See next page for Problem 3)
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Unformatted text preview: 3.0 Complete the entries of the table given below, where b, ϖ , and φ are real numbers. Time-Domain Function f(t) Laplace Transform L [ f(t) ] 1 sin( τ 29 Σ(τ 29 2 cos( τ 29 Σ(τ 29 3 2 βε-βτ χοσ( ϖτ 29 + 2 γε-βτ σιν( τ 29 Σ(τ 29 4 (2 β 29 2 + (2 γ 29 2 ε-βτ σιν( τ + 29 Σ(τ 29 ϖηερε = αρχταν Hint : See class notes. Note : The L [ f(t) ] should contain β and γ , but should not contain φ . 5 2 χοσ( 29 + 2 σιν( τ 29 [ ] Σ(τ 29 6 (2 29 2 + (2 29 2 σιν( τ + 29 Σ(τ 29 ϖηερε = αρχταν Hint : See class notes. Note : The L [ f(t) ] should contain β and γ , but should not contain φ ....
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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.

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Homework 03a - Laplace Transforms Table - 3.0 Complete the...

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