Figure below shows a schematic diagram of seat suspension system. a) Derive the equations of motion for a quarter car suspension system using an appropriate free body diagram. The system must be at least a 2nd order system. Assume that the Force u is the input to the system and the vertical motion Y of the body and is the output, obtain the transfer function Y(s)/Z(s). b) Based on your answer in (b), derive the state equations, output equation and represent those equations in a matrix form. Driver mass, www www C b Seat mass, 2 Driver displacement Seat suspension Seat displacement Z(1) Cabin floor displacement