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MECH 466 - Lecture2-LaplaceTransforms-2009W

unit ramp function unit ft ft t 0 integration by

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Unformatted text preview: Unit ramp function Unit f(t) f(t) t 0 (Integration by parts) 2008/09 MECH466 : Automatic Control 5 Integration by parts 2008/09 MECH466 : Automatic Control 6 Ex. of Laplace transform (cont’d) Formula Formula Unit impulse function Unit Width = 0 Height = inf Area = 1 f(t) f(t) t 0 Why? (Memorize this!) Exponential function Exponential f(t) f(t) 1 t 0 2008/09 MECH466 : Automatic Control 7 2008/09 MECH466 : Automatic Control 8 2 Laplace transform table Examples of Laplace transform (cont’d) (Table 2.1 of the textbook) Sine function Sine (Memorize these!) Cosine function Cosine Inverse Laplace Transform Remark: Instead of computing Laplace transform for each function, and/or memorizing complicated Laplace transform, use the Laplace transform table ! Laplace (u(t) is often omitted.)...
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