Question 3 6) Find the Inverse Laplace Transform of: S +2 X(s) ROC: – 4 < Re(s)< -3 s2 + 7s + 12 7) Determine The Laplace Transform Y(s) of y(t), when y(t) = x1(t – 2) * x2(-t + 3) x1(t) = e-2tu(t) = e-3tu(t) e x2(t)
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Transcribed Image Text: 3 6) Find the Inverse Laplace Transform of: S +2 X(s) ROC: – 4 < Re(s)< -3 s2 + 7s + 12 7) Determine The Laplace Transform Y(s) of y(t), when y(t) = x1(t – 2) * x2(-t + 3) x1(t) = e-2tu(t) = e-3tu(t) e x2(t)
More Transcribed Image Text: 3 6) Find the Inverse Laplace Transform of: S +2 X(s) ROC: – 4 < Re(s)< -3 s2 + 7s + 12 7) Determine The Laplace Transform Y(s) of y(t), when y(t) = x1(t – 2) * x2(-t + 3) x1(t) = e-2tu(t) = e-3tu(t) e x2(t)
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1) {:[(s+2)/(s^(2)+7s+12)=(s+2)/((s+4)(s+3))=(A)/(s+4)+(B)/(s+3)],[" When "s=-3=>B=(-1)/(1)=-1],[" When "s=-4=>A=(-2)/(-1)=2quadL^(-1)((1)/(s+a))=e^(-at)],[(s+2)/(s^(2)+7s+12)=(+2)/(s+4)-(1)/(s+3)]:}Applying inverse laplace transform,{:[L^(-1){(2)/(s+4)}=2e^(-4t)L^(-1){-(1)/(s+3)}=-e^(-3t)],[L^(-1){(s+2)/(s^(2)+7s+12)}=-e^(-3t)+2e^(-4t)]:} {:[y(t)=x_(1)(t-2)**x_(2)(-t+3)],[x_(1)(t)=e^(-2t)u(t),x_(2)(t)=e^(-3t)u(t)]:}From laplace transform pairs and properties{:[e^(-at)u(t)longleftrightarrow(1)/(s+a)],[x(t)longleftrightarrow x(s)],[x(-t) ... See the full answer