(Solved): A linear time-invariant system is described by the second order differential ...

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A linear time-invariant system is described by the second order differential equation \[ \frac{d^{2} y}{d t^{2}}+5 \frac{d}{d t} y+4 y=u . \] (a) (i) Compute the transfer function \( H(s) \) of the system. [3 marks] (ii) Is \( H(s) \) a Bounded Input Bounded Output (BIBO) stable transfer function? Justify your answer. [3 marks] (iii) Assume that the initial conditions are all zero, and that \[ u(t)=\left\{\begin{array}{ll} 0 & \text { if } t<0 \\ 1 & \text { if } t \geq 0 \end{array}\right. \] Give an expression for the value of \( y(\cdot) \) at time \( t \).