The steady-state response is due to simple poles in the j axis of the s-plane coming from the input. Suppose the transfer function of the system is: H(s)=Y(s)/X(s)= 1 / (s+1)^2 + 4
a. Find the poles and zeros of H(s) and plot them in the s-plane. Find then the corrosponding impulse response h(t). Determine if the impulse response of this system is absolutely integrable so that the system is BIBO stable.
b. Let the input x(t) = u(t). Find y(t) and fromit determine the steady state solution.
c. Let the input x(t) = tu(t). Find y(t) and from it determine the steady-state response. What is the difference between this case and the previous one?
d. To explain the behavior in the case above consider the following: Is the input x(t) = tu(t) bounded? That is, is there some finite value of M such that |x(t)| < M for all times? So what would you expect the output to be knowing that the system is stable?