Question

Determine L^-1 {F}. I also attached the tables linked in the problem. Thank you!

Determine & '{F}. 2 4s + 44s + 92 F(s) = (s – 1) (s? + (s? +65 + 13) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 2"{F}=0

Answer 1

solution : we have given that Fis) - 452 +445 +92 0) (S-1) (S? + 6 S +13) need to solve (fisi) First of partial of all will find faction decomposition decomposition of f(s). ha thits Let + S-) f(3) = 45² +445+92 A Bstc s? +68+13 (5-1) 252 +65 +13) শি 452 +445 +92 Als?+05+13) +(BS+C)(5-1) 13-1) (s? +65 +13) (S-1) Cs? +65 +13) (2) bi दिया - 45+445 +92 = As² + GAS +13 A + B is? B stesc comparing the both sides coeffi cients of get powers of S we A+ B = 4 (3) 6 A - B +5 = 44 (५) 13 A 92 (5) Adding (4) & (5) get 6A- B + C +13 A - 44+ 92 19 A- B - 13 6 (6) Now adding (31 and (6) we get

4 +136 A + B +19 A - 20 A = 1.40 V > A = 7 from (3), 11 Ba have we 4-A - 4-73-3 from have C- 13 A - 92 (5) we 13171.925 91-92 --- we have As 7, B - -3, (-) Fis) 7 -3 S-1 + S-) s? +65 +13 ! ( By (21) 11 7 3 st to ratos S-1 (5?+2135) + 9+ 4 3 st 1 1 S-1 (5+3) 2 +22 7 3 S-) 3 ( 5 + 5 $) (5+3)2 + 22 7 3 cs + 3.-3 +) $-) 15+3)2 +22 =123(18+344 93 ) S-1 (5+3)2 + 2?

= f(s) = 7 S-1 3 (5+3) . 38 34(-4):37373 (5+3)+22 ។ fis) s-1 3 15+3) (5+3)? + 2? + 8. 1 (5+3)+22 ㅋ 2-1 Fisi) 7 3 (5+3) I'{ s-1 (5+3)2 + 2? 8 (5+3)+22 **(+) - 3 **4*3*** ( 1st 3) = +2 + 8 L ) t 7e - 3. e 3t casat + -34 Njoo Sin at 2 Llet)=1 t ĪT 1" (5) - e s-1 de at cos bt) S-9 11 키서 allo (sa)2 +6² S a e a at (s-a²+ b cos bt and Lle Hleat sin bt) b (S-a) +6²

= 2 ( isosto) Leat Sinbt (5-9)?+6+ b Thus - < (fis)) = 7 et =7 et a. 3 e 34 Cosat -3t + Че sinat t L" (FIS)) Tet 14 sinat- 3 castle 3t the required inverse laplace to and form of given F(3). is

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