Question

Question 9 3 pts The Laplace transform of the piecewise continuous function J4, 0< < 3 f(t) is given by 2, t> 3 2 L{f} (2 - e-st), 8 >0. S L{f} (1 – 3e-), 8>0. 8 2 L{f} (3 - e-s), 8 >0. S L{f} = (1 – 2e-st), s > 0. None of them Question 10 3 pts yll - 4y = 16 cos 2t To find the solution of the Initial-Value Problem y(0) = 0 the y (0) = 0 Laplace Transform was applied and it was obtained as "Laplace Transform" of the unknown function y=f(t), the following: S L{f(t)} 2s S 2 1 s +2 $2 + 4 1 1 L{f(t)} + 2s 82 +4 S- 2 $ + 2 None of them 1 S 2s L{f(t)} = S- 2 S + 2 82 +4 2 2s L{f(t)} + 1 $+4 S 1 82 +4

Answer 1

First I have written the rule and then find the solution.

Option

Non of them is correct

For both problem.
Note.. Definition function of Laplace fit). transform of OD L [feti] = 5 est. flt).elt ; so Solution. Griven that fet)= { 4 olt <3 La 2 , t>,3 Now By definition L[ f(t) soestf(t) at { Noc Now By givea fiti -st + se fltl.lt sest fits at 3 3 s è st 4 odt + s èst 11 2.dt 3 ost 243 + 1*** dt dt + 2 s è 9 {. Seandx -S 3 -ax =e -a 4 Center I 2 [ est c2eº] +) cém-es] 4 [ess - 1] - 2 co-835

pare a 35 L [ f(t)] = -4e35 + S e 3 li o - 81- e35 gly + inle crè - L {f} glu (2 - 035) This is our Laplace transformation piece - wise function fit) of geven Hence Last of front correct. Leel Nou of them solution 6 Noste - since that we know L[1] = yes) I[f'] = suges) - Yeo) and LEY"]= s²yes) - syeol y'CO) and S L [Cos at 7 = s²492

Griven that page 3 = y"- 44 = 16 cosat / 7101=0, yco=0 Now Taking side transform Laplace then both cue get Il yll – 44) L( 16 Cosat) => Llyl)- 4 hey) 16 Licosat) = ) say(s) -sy1o) - Y60) 4 yrs) = 16. s s²+ z2 2 =) s? yes) - SXO-0- 4 yes)= 165 s²+4 = ) (52-4) y(s) = 165 s² + 4 = ) yes) = 165 (52-4) (5²+4) =) Ly(t)) = { yes) = Lly) 165 (S2_4) (5²+4) =) I (fit)) = *: y=f(t) 165 (52-4) (52+4)