Consider the following first order dynamic system: 78 +21x = 36 uſt) a) Find the transfer function from U(s) to Y(s). b) What is the system time constant? What is the DC gain (i. e. static sensitivity)? c) Assume that input u(t) consists of a step function and a ramp function, such that | u(t) = 6 + 2t. Without solving for y(t), qualitatively describe the steady-state response you expect from this linear time-invariant (LTI) system. d) Based on the input from part (c), and assuming zero initial conditions, solve for y(t). e) State whether the response of part (d) consists of a free response, forced response, or both. Explain your reasoning in 1-2 sentences.