(Solved): Problem 2. For a simple second order system that is represented with the block diagram on the rhs, ( ...

Problem 2. For a simple second order system that is represented with the block diagram on the rhs, (a) Obtain the difference equation relating the input \( x(k) \) to the output \( y(k) \). (b) Obtain the transfer function \( G(z) \) relating the input \( X(z) \) to the output \( Y(z) \). (c) Find the poles of the transfer function. (d) Determine if the system is stable. (e) What would be the steady-state value of output when the input is a unit step? Hint: Use the Final Value Theorem.