Question: 4. (30 points) Consider a system defined by a differential equation whose homogeneous response is given by yh(t) = sin( 3 t) and answer the

4. (30 points) Consider a system defined by a differential equation whose homogeneous response is given by yh(t) = sin( 3 t) and answer the following questions. (Spring 2020 - Midterm 2 Problem 2) (a) What is the order, N , of the corresponding differential equation? (b) Find Q(D), the state polynomial, for the differential equation. 1 (c) Assume P (D) = 1. Write out the full differential equation. (d) Calculate the system's transfer function. (e) If the given system is LTI and the input to the system is given as x(t) = 4et, then, calculate y(t): y(t) = ( ) ( ) + 2 9 e( )

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