Use the result in Q4 to find the response, c(t), to an input, r(t) = u(t), a unit step, assuming zero initial conditions. Find the transfer function, G(s) = C(s) / R(s), corresponding to the differential dc 3dc dc dr dr equation +3. +7 +5c = +4- +3r. dt dt dt dt dt Find the differential equation corresponding to the transfer function, 2s+1 G(s): s +65 +2 Find the ramp response for a system whose transfer function is G(s) = S (s+4)(s+8) Write the differential equation for the system shown in Figure 1 R(s) s5+254 + 4s3+g2+3 so + 755 +354 +253 +2+3 S C(s)