3. Given is the system in the figure below. Determine a transfer function relating the output C(s) to the input R(s). Then, determine the value of k, such that the

damping ratio 5=0.5. Calculate also the rise time tr, the peak time tp, the maximum overshoot M, and the settling time t, for a unit-step response. Find an analytical expression of c(t) for a unit-step input, given the calculated value of k, and plot the diagram. Finally, study the effect of k on the response of the system to a unit-step input via a parametric analysis: make ented MATLAB®scripts and the image of the plotted data. What is the value of k such that the system is critically damped?