A cart with negligible rolling friction is connected to a spring (k-2) and a damper (b-0.5) as shown in Figure 3. An input force u(t) is applied. The mass of

the cart is M, (1kg), and its displacement is x(t). Answer the following questions: \text { Determine the transfer function, } G(s)=\frac{X(s)}{U(s)} Use MATLAB to simulate the response of the system to a unit step input ; :) Design an appropriate controller such that the following performance specifications are met : Settling time (2% criterion) less than 4 seconds; An overshoot of less than 0.5B %3; A steady state error to a unit ramp input of less than 10%. Show your full workings and include any relevant MATLAB codes and figures to validate your design.