Question

95 | 100% 13:25 AM + Expert Q&A + M TOV./4's 10 cost Volls using the Laplace Transform 07

solve using laplace transform. switch closes at t=0

Answer 1

Hey there! Hope the solution is clear. Thank you and all the very best :)
ict) 10 cost v 12 10 V elw 1 H Let us convert the circuit in Leplace domain. I (S) los $21 lo S S 10 S al s² + 1 T (5) 2 St I 10 10 S SIS+1) (5+1) (5²+1)

S+1 S Now, 10 S(5+1) 5(5+1) 10 S s+1. Applying inverse Lapluce transform → 21 Sisons) 10 (1 -^)(+) I(5+1) 1os for using partial fraction expansion, (5+1)(+1) 105 А BSc + (s + 1) (5²+1) sti s² + 1 10 S a A (5²+1) + (BSc) (5) Put s--1 - 10 2 A (2) to A 2-5 put sa o o A10+ 1) + (6 + c) (0) o A + c 23 C = - A - 5

put sal A (2) + (B+C) (2) 10 10 2A + 2B + ac 2 -10 + 2B 10 > Be 5. TOS 55 - 5 5 + N St1 (s + 1) (3² + 1) 5 55 5 + St1 s? +1 s²1 Applying inverse taplace transform 10 s 27 (5+1) (5²1) ] =(-5et + 5 cost + 5 sin + 5 sint) alt) Hence 36+) (10-2) + (-se's ust5 bint)] urt) - i(d) 10 - 156*5 cost. 5 bint) utt)