Question

determine Laplace transform of a-d

(a) f(1) = (1 - 4)u(t - 2) (b) g(t) = 2e-4eu(t - 1) (c) h(t) = 5 cos(2t - 1)u(t) (d) p(t) = 6[u(t - 2) - ut - 4)]

Answer 1

FIS) 5 - 2025 v Laplace trasform Srls = 10 fev erot at? formula a f 4+1 = (t-4) U(+-2) but the value in equn FIS) = SW (t-4) ult-2) estat → 2 to co U (+-2) * t range 2 <tloo مس ult-2) = otherwise two function integration Sfitz = fil fods - Chemin Stas F (S) = 1(t-93&st dt = 14-vjr 1046-4! -st .dt (t-4) e-st s -S - (1.95 $) F15) = 2x0-0 +(2-1) .25 + 52 -25 e s 52

-at ult-1) 6 geH= = 2e using formula of Laplace dt 915) - Lo quest - J^2 eftult-1) estali Ietlo U16-1)- other Ult-indt = 21° e-(4+5) dt =24,59€- (5+4) = 2 [ :) . e-(s+4)t 7 ao - (5+4) o + é (5+4) c2 2[0+ st4 2e-15+9) ģis) ste Ang h(t) = 5 Cos (24-1) ult) Cas (A-B) = Coy A Cas B+ Sin A Sin B Cas (24-1) = Casat cosi't sinat sini Cos I'=1 Sini = 0.0174 Cos (2+-1) = Cosat +0.0174 Sinat

using table of Laplace transform ILI Cas wot S s²two? Sin not a LT Wo 5²+ug? htl=5 Cosat ult) + 0.087 Sinat ult) taking taplace foam from HIS) - 5[***] + 0*087[***] 5 55 +0:174 HIS) - S2+4 Ans d P(+1=6 [ulta +-2) - Ult-4) =6ult-2-bult-4) 6U17-) 6 Ult-4) 6 TE 4- t 2 Plt) 6 >t 2 4

Pltl= 2 <ta4 6 1 otherwise 4 dt PIS) = 16 6e-st 2 4 = est 6 2 نی -s -25 56 e te [ PIS) = 6 -s P(S) - 6 & [e-es Ang