Consider the first-order linear system (constant coefficients a, b, and c) dot x (t)=ax(t) bu(t); y(t) = cx(t) We will consider two instances of this linear system: system S_{1} with parameters a = - 1 , b = 1 , c = 1 and system S_{2} with parameters a = - 10 , b = 10 , c = 1 . (a) Recall that the frequency-response function G(omega) for the above first order system is G(omega) = (cb)/(j*omega - a) Compute the magnitude |G(omega)| and the angle angle(G( omega)) for each system and for omega = 0, 0.1, 1 and 10. (b) What is the time-constant and steady-state gain (from u y) of each system? How is the steady-state gain related to G(0)? () For each of the following cases, compute and plot y(t) versus t for the i. S_{1} with x(0) = 0, u(t) = 1 for t > 0 . S_{2} with x(0) = 0, u(t) = 1 for t >= 0 . S_{1} with x(0) = 0, u(t) = sin(0.1t) for t >= 0 iv. S_{2} with x(0) = 0, u(t) = sin(0.1t) for t > 0 . S 1 with x(0)=0,u(t)=sin(t) for t >= 0 vi