MAE147-lecture+10

MAE147-lecture 10 - MAE 147"Vibrations Lecture 10 Instructor Professor Andrei Shkel Email [email protected] Office EG4208 Before we get started For

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MAE 147 “Vibrations” Lecture 10 Instructor: Professor Andrei Shkel Email: [email protected] Office: EG4208
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L10-2 MAE 147 “Vibrations” Professor Andrei M. Shkel Winter 2008 Before we get started ± For this week ² Starting Chapter 5 ² HW5 due today ² No Quiz today ² Midterm after lecture, due before lecture on Wed., Feb.13 ² Exam covers Chapters 1-4, Lectures 1-9 ² Reading: Sections 5.3-5.5 (due Feb. 13 th ) ± Last Time ² Response to Base excitation ² Transmissibility ² Bandwidth ² Instrument Design
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L10-3 MAE 147 “Vibrations” Professor Andrei M. Shkel Winter 2008 Lecture Outline ± Laplace Transform ² Definition ² Application ² Laplace Transform Pairs ² Input Functions
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L10-4 MAE 147 “Vibrations” Professor Andrei M. Shkel Winter 2008 Definition of the Laplace Transform f ( t ) is function in time domain F ( s ) is function in Laplace domain Laplace transform L { f ( t )} is defined as {} = = 0 ) ( ) ( ) ( s F dt e t f t f L st ) ( ) ( ) ( s F t f t f L ⎯→ ω α i s + = Basic Properties of the Laplace transform L { f ( t )} 1. Linearity 2. Transform of Derivatives 3. Transform of Integrals ) ( ) ( ) ( 1 s F t f s F L ⎯⎯ { } { } { } ) ( ) ( ) ( ) ( 2 2 1 1 2 2 1 1 t f L c t f L c t f c t f c L + = + ) ( 1 ) ( 1 ) ( ) ( 0 0 0 0 s F s dt e t f s dt e d f d f L st st t t = = = ∫∫ ττ ) 0 ( ) ( ) ( ) ( 0 0 0 f s sF dt t f e s t f e dt dt df e dt df L st st st = + = =
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This note was uploaded on 04/07/2008 for the course MAE 147 taught by Professor Shkel during the Winter '08 term at UC Irvine.

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MAE147-lecture 10 - MAE 147"Vibrations Lecture 10 Instructor Professor Andrei Shkel Email [email protected] Office EG4208 Before we get started For

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