Tabela de Transformadas de Laplace

Table of Laplace Transforms fLFs Fs 1 F0 ftFs Fsft 1 1 i 2 ef tL s sa 3 tf n123 a 4 PP pl Test s s 5 vt vn 6 2 n123 1352n1 Ve 2s 2 gt a s 7 sin at aa 8 cosat vag 2as sa 9 tsinat s ay 10 tcosat 4a 2a 2as 11 sinatatcosat ea 12 sinat atcosat ee ss a ss 3a 13 cosatatsinat esa 14 cosatatsinat era 15 sinatb ssinbacosb 16 cosat b s cosbasinb sta sta 17 sinh at a 18 cosh at a at b at sa 19 e sinbr say 4b 20 e cosbr sap ab ats b at sa 21 e sinh br sa 22 e cosh bt sa n 23 te n123 say 24 fct 5 c le 95 Me tutc e 26 6tc eo Heaviside Function S Dirac Delta Function 27 U t ftc eFs 28 u t gt eLgtc 29 ef t Fsc 30 tft n123 1 Fs 1 w F aL A f0 Fwdu 32 fi Fvyav FG es at 33 ft eat FsGs 34 ftTft 0 le 35 ft sF sf 0 36 ft sFssf 0 f0 37 ft sFssf 0sf0 sf 0 f 0 Table Notes 1 This list is not a complete listing of Laplace transforms and only contains some of the more commonly used Laplace transforms and formulas 2 Recall the definition of hyperbolic functions ee ee cosh t sinh y y 3 Be careful when using normal trig function vs hyperbolic functions The only difference in the formulas is the a for the normal trig functions becomes a a for the hyperbolic functions 4 Formula 4 uses the Gamma function which is defined as ex tl t J ee dk If 7 is a positive integer then Tn1n The Gamma function is an extension of the normal factorial function Here are a couple of quick facts for the Gamma function pl pI p pn Pptl pt2ptn1 P1p2ptn 1 r5 Vi