Question

13. (20%) Calcule la transformada de Laplace de las siguientes funciones: o silst<1/ a. f(t) = »= { cost sit 23 b. f(t) = e-t sint

Answer 1

Definition: LF(t) Here, Lif(t)} = + jest Cost dt ㅈ 18mntētu @comb criven ft) ost La Cost: tan we have Find Lif(t?. F(t) at est. o at & pest cost at I 5) L} Ft) o.de Cost at A - sint dt a 졸 -SXZ - LIFE Ebounded To T in ei Zero (ié o$costajad + 2 a 2 Jo est cost alt = LITH} = best cost at L}F(t)} = cost lest at jelente) Sestanet LEW) = leosten - (Cost a 2 2 J

lat 2 est dt = LF(t) = I cost estat zero in Eli ieco and Imm)-1 > Low) = (kemused x 94-10 x 3 )- Jamt et de =>L}FC)} = (o-o]-7} sint e jest at) +}lent cette - Cost = LIFE)= - = ? Come soo) Coma 1 Jeast -) Lipwls - (escended x 3) (***) * 410? 274) + *270173 -40+ =) (1+) 218? no es tu ? ?5() és 2. 1803? len smo) ets S? L?FC)] L

Sol? Crinen f(t) = éteint we have to find find hetsint} when s> Theory! If L} f(t)} = F(8) Then, Leat F(t)} F (S-a) S2+a i.e. If Then, which F($) is Laplace transform of 40, F (S-a) is the Laplace transform of eat f(t). is called d. first shifting theorem LIFH)} = Lisint] L1961)) = • Lisinat} = 52 +12 sta Here, 1 a » L?F(t)} = FS) (lay) H Here, Focal Then, Letsint? = F(S+1) - Liet birit? (5+12 + 1 N =) Llet sint} = 2125+1+1 - 4e temp? = 272513

Thanku Any doubt please comment I'll help ou.