Question

2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet

Answer 1

Solution 1 Taking = 8 82 +92 (1) f(t) = 44+ Cost3t) + 3e-24 Labelace Both side =) L{fles} 4194 + l{COS(34) + 3L{ 4-23 Since L(th)= hel ghti L(Coxat) - lleat) 1 (sinat) = 8392 Now using above Formula to solve = L{f(t)} = 82403)2 L{ f(+]} 8249 Answer = 8-9 a 8 + f 441 84+1 3 8+2 5 ) 4! S . + + 3. 8+2 85

2 ert 3 & 2 e (2) h(t) = (1-e3+)2 2) h(t) = I +(83+)2, 223+ =) hld) = It e Takeng Laplace both side Lę niej L(59 +1(861) – 211634) L {h(t)} 8-6 Andwer → = - 2 8-3 8 t &in2t (3) glut) = (since Coxat=1-2 sin2t sin?a= I-coret 2 Thent tr gleda + [ { - Cos24] if 4{{{4}}=F(8) 9(2)= £t £ Copet L291413 41(4)- LC0x24 {[ +++ + 9+ - [rd (g) » - FRI] zse + {[(849).00 $(22) 2+ [ Atelings? LE&UM} = 282 + z 2 Answer (82+4)2 = نکا

3 (4) n(A)= e 2t Cox (534) - f2et L{hle] L{e=24C08(13 A)} -4(et 42) Since Leat flas} = F(5-a) when L{f(a)}= F (S) Now using The formula . L{hlet} Cos (53I)}-2(ette) L { cox 534} = $2+ 1 { & 2* Co83-4} = (8+2) $+8+2) (8+2)2+3 above L{ezt 8 +93) 2 and L{+2} 241 2 C 2+1 83 Let +23 = (8-13 Hence 2 L{hlal} - (8+2) (8+2)2+3 8-13 Answer Please like me for good cf score and ff any problem in This solution Then comment me.