Question

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Find Laplace Transform of the following function showing all the stepso fct) = (t + et cash (2t)) it. sinklets of

Answer 1

f(t) = (t + est cosh(2+)]{+ t sinh at + 7+ $ l (flt)) = Il + tedt coshat) + llt sinh2+) + L17) Now solving llt + e 3t cosh at)? - Now (it te at to shat) ² - 0 iť + e 4t coshat + led twosh.at - Now sinhat = at - liloo Hoo cosh 27 - edt

2 7h Sulostituting value of coshat i 0, TH+ est cosh at) elt te* (* te>'))* --**4 + 1*"* = (st 11 te")* - (at + D? + 2*8* + de "t (2+ +1) 7 ( 4€+1+46 + e*t +44&4 + de 87 z ť + 1 + t test + te" + eshte Itteft cosh at) = ((??) +114) + llt) + Lleny - tllte) + Lent) 4+2+1+ 4 + & 1 + + + 1 45 + 2 53 + 1 1 52 + + 1 418+8) S+4) #218+4) fi teftet) - ] $ + 4 + 4 + 41s + 5) *isty ja talsty) = ®

Know S 4 Now lt sinh2t), We know that L (sin b 2 t) : Llit sinbat) CD lau) Definuje 20 -25 L (5²-4) ² S -4 [ 1 [sinhat) - Ll+ft)) -F15) tint 7t int e can be written as Jn 7]t La Inab = bina] Now 117 = Llent) t 1. = 1 Filleat) = 11 S - in 7 L s-al

From © © ¢ 217 Lt)) = + 1 + 1 + 1 + 1 a +45 + Ś2 - 41S+8) (sty)2 + + 21st4) 45 (5²-4) ² + 1 s-107 1