Question: Consider a LTI system with transfer function (a) Determine if the system is BIBO stable or not. (b) Let the input be x(t) = cos(2t)

Consider a LTI system with transfer function

s? + 4 Y (s) H(s) = X(s) s((s+ 1)² + 1)

(a) Determine if the system is BIBO stable or not.

(b) Let the input be x(t) = cos(2t) u(t) find the response y(t)and the corresponding steady-state response.

(c) Let the input be x(t) = sin(2t) u(t) find the response y(t)and the corresponding steady-state response.

(d) Let the input be x(t) = u(t) find the response y(t)and the corresponding steady-state response.

(e) Explain why the results above seem to contradict the result about stability.

s? + 4 Y (s) H(s) = X(s) s((s+ 1)² + 1)

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