Consider the system r(s)-g(sx(s) with transfer function g(s) 4/s^2 +3s +2 . let r(t) and x(t) be the inverse laplace transform of r(s) and x(s), respectively. (similar to example 3.1) 1a. find the differential equation corresponding to the transfer function g(s). (500) lb. find the characteristic equation and the poles of the system. (590) 1 c. find the damping ratio ç , the natural frequency a,, and the steady-state step response xss of the system. (5%) ld. is the system overdamped? critically damped? underdamped? or undamped? (590) le. assume the initial conditions x(0) 0 and (0)-0, and let the input r(t) be an unit step function. find the output response x(t). (15%) if. plot the constant term, the two exponential terms of x(t) and the sum of these three terms versus t on the same graph. discuss how these two exponential terms relate to the system poles, and how the constant terrm relates to ' (15%)