Answer:
(A) [tex]X(S)=\frac{1.25}{S^2+4}[/tex]
(B) [tex]X(S)=\frac{0.2941}{S}[/tex]
Step-by-step explanation:
We have to find the Laplace transform
(a) x(t) + 7 x(t) = 5 cos2t
Taking Laplace of both side
[tex]X(X)+7X(S)=5\times \frac{2}{S^2+4}[/tex]
[tex]8X(S)=\frac{10}{S^2+4}[/tex]
[tex]X(S)=\frac{1.25}{S^2+4}[/tex]
(B) [tex]x(t)+8x(t)+25x(t)=10u(t)[/tex]
Taking Laplace transform of both side
[tex]X(S)+8X(S)+25X(S)=10\times \frac{1}{S}[/tex]
[tex]34X(S)=\frac{10}{S}[/tex]
[tex]X(S)=\frac{0.2941}{S}[/tex]
