Question

Only #23,27,33,41 step by step neatly please

In Problems 5-21 through 5-30, determine the inverse Laplace transforms of the functions given using Table 5-1 (and Table 5-2, if appropriate). 5-21 V(s) = 5+ 3 3 4 5-22 1(s) = 2 + + SS 5-23 32 F(S) = 2 + 64 SYE 6-24 10s 1(s) = 2 + 25 5-25 V(s) = Os + 15 8² +9

Answer 1

23) FCS) FC Barcelona We have, L[ Showt] = Here, was F(S) = + = 40 LIF (S)] = f(t) = 4 . dinst . . f(t) = 4 ainst 33) UCS) = 35 + 135 +8 s(s+35+2) v(s) - 35 + 135 +8 S (5+1) (S+2) Uring partial fraction expansion 35 + 135+8 – A & B & c S+2 +38+135+8 - A (sti) (s+2) + B. S (S+2)+C.s(s+) S=0 ?A=8 = A=41 S-->) -B = 3-13+8 = -2 2 B-2

S= ((-2) (-1) = 12-26 +8 = -6 Sta (s) + S + Spa We have, L[1] = 3, the J = 1 L {ves)] = 4 + 2. et + 2. e2t. . o(t) = 4+2 (et te 2) 41) U (s) = 20 (544) s(s+) (5+25+2) UCS) - 20 (8+4) - 205 480 s(s+l) ($+25+2) s(s+i) ( 5+25+2). thing Partial fraction expanion, 203 +80 SCS+i)(3+25+2) Ŝ SH Std => 20$+80 = A (sti) (s+25+2) + B.S (S+25+2) +(CS+D) S(St) S=O A = 40 5:--)-8=100 B=-100) S-2 C = 60 D-40) 5+2 5+2

. V(S) = 40 - 100 & 605 +40 8²+28+ 2 V(s) = 40 - 100 s st1 & bos 8²+25+2 & 40 5+25+2 Expaneling bos 5+25+2 = 60.5 (Stift1 = 60 (SH) - (5+1)²+1 - bo. (St) (Stift - 60. I (SH)² + 1 1 8+25+2 [Stift S+ Expanding 40 – 40 2 (Stift ..v(s) - 0 - 100 + 60.(s+i) -60.1 + 40.! (St) 1 (S+1)²+1 (8+1+1 We have, K'L', He, 1783-etace), | certi J = et sin(t). :.L[us] = 40 - 100 € + 60. e cost – 20. et aint V(t) = 40 - &t (100 - 60 cost + 20 mint)