Question #4 : Input output relationship of a linear time invariant continuous time system having zero initial conditions is given with the following differential equation d³y(t) d²y(t) - 5 dt³ dy(t) +9. dt - 5y(t) = x(t). dt2 Obtain output of the system for each given input. x1(t) = 3[u(t) – u(t – 2)]. a) b) c) x2(t) = 2e-3lu(t). x3(t) = x,(t) + x2(t – 2).

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Solve for x(t) in the system shown in the figure below if f(t) is a unit step

Let x(t) is an input to a continuous time linear time system S and y(t) is the output. The input-output relation is given by, x(t)=e^ j3t longrightarrow y(t) = j * e ^ (j * 5t) x(t) = e ^ (- j * 3t) -> y(t) = - j * e ^ (- j * 5t) What is the output y(t) when the input x_{1}(t) = cos(5((3t)/5 - 2))