1. Find the inverse laplace of the following: 12 a. 4 S 1 b. 52 +...
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s? +45-5 b. F(x) = s(s? +2s + 5) 2. (10 points) Determine if the following differential equation is exact. Be sure give a reason for why or why not. If it is exact, solve it. (xy? + 3x y)+(x° +xºy)y'=0 a. F(s)= (1-25)e-
Find the inverse Laplace transforms of (a) (b) (c) s 1 (2s +1) Y(s) = (822 5s + 8 (2s - 2) 21) Y(s) = Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) = (5-7)2 s 1 (2s +1) Y(s) = (822 5s + 8 (2s - 2) 21) Y(s) = Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) =...
1 +s Find the inverse Laplace transforms of the following: a. F(s) = a (s+2)2 b. F(s) = -25- Hint: Complete the square in denominator 2s -1 s2-2s +10
Questions 7-12: Find the inverse Laplace transform of the following. 1) F(s) = s+7 e +2)e(s+8) 10.) F(s)+2 s2 +3s +6 2s + 22 8.) F(s)--s428- 11.) Fo) 4s+13 12s +108s2 +552s +1008 +12s +107s +426s+754 34s2 +119s+71 12.) F(s)
Q2 [20 pts]: Find the inverse Laplace transform of each of the following functions. 2s +3 (a) F(S) = 53 +45 (b) F($) = 52 - 68 + 13
4. Find the inverse Laplace transform of 2s + 24 F(S) = (s +1)(s? +65 +34) Solution:
question b a) Find the inverse Laplace Transform of: 145+23 F(s) 52 +55+4 (7 marks) b) Determine ift) in the circuit shown in Figure Q2(b). 2H 202 i(t 102 1) cut) IF Figure Q2(b) c) Determine the mesh currents, I, and 12 in Figure Q2(c) in the s-domain (8 marks) 102 IH 10 st V 0.25 H 13 ΤΩ Figure (20)
1. (10 points) Find the inverse Laplace() = C'{F} of the following: 4 6 1 a) 2 F(S) + s 8 + 8 S b) 2 F(s) c) 2 F(S) (s - 1)(8-2) 8 +3 32 +2s +5 782 +238 +30 (8-2)(2+28+5) d) 4 F(s) =
help 1. (10 points) Find the inverse Laplace f(t) = --'{F} of the following: 4 6 1 a) 2 F(s) + S 8 +8 S b) 2 F(s) c) 2 F(8) (8 - 1)(8-2) 8 +3 $2 + 2s +5 7s2 + 23s + 30 (8-2)(82 +2s + 5) d) F(s)
Find the inverse Laplace transformation of: a) F(s)- b) F,(s)--2 c) F(s) = 2,242 4 s2+6s +5 s2 +3s +1 3+2s+s s2 +9s +18 e) F(s)--一5 2s4 +12s+90 (s+2)(s +2s+2)