Question

1) Find the impulse response of de VCE) + 6 mV (t) + 5y(t) = x(t) + 3x(t)

Answer 1

ce + 6 (+57(4) = 4*4 + 3x(4) Find Impulse Response of the system > Impulse Response of a system is response when input is 8(t) of a (u) = 8(t). Now In Laplace domain 4” xº) = (s) dth If all Initial condetion is o. I [8(t)] = [[xft] = 1 Now > Apply Laplace Transform to Equalurin sY(s) + 68Y(s) + 5 y(s) = S X(s) +3X() = y(s) = (s+3) (s) $) T8 °763+5) Now X(s) = { [« (+)] = [[$(+)) = 1 S+3 Y(s) = $4465+5) (52+65+5)

Y(s) = _5+3 (5+5)(st) :: $2+65+5 = (3+5) (sti) Apply Partial fraction is+5)(s+I) (s+5) IST → (3+3) = A (5+1)+ B (+) - At s= -1 > -1+3 = A(+1+1) +8 (+1+5) = B = 2 = 0.5 At s= -5 3-5+3 = A(-5+1) + BC-5+5) →-2=-4XA +0 A = 0.5

so y(s) = 1/2 (sts) + 2 (st) sta Now I'[ k] = ke duley Alpbly Laploce Invese to Y15) YC0 = ý cet & Jure J (0 = 0-5 [€ 54 e tj uct