Consider the system shown in the gure: a) Identify possible \"State Variables\" and determine the order of this system. b) Find the \"State Equations\" c) If all initial conditions are zero, take Laplace transform and write the state equations in Laplace form. d) Convert the \"State Space\" equations into a single \"Inputx'Output\" in time domain where the input is the force applied to M1 and the output is the distance x1(t). e) Find the \"Transfer Function\" of the U0 model: H (s) : :15) : :2; t) Find the roots of the numerator, N (S) and call them zeros (21, 22, .. ) and the roots of denominator, D(s), and call them poles (pl, p2, ...). Draw a Pole-Zero map on the splane. Mark the location of each pole with an 'x' and the location of each zero with \"o\". g) Comments on the behaviour associated with each pole. h) Use the Partial Fraction Expansion method to nd the system impulse response, h(t). i) Use inverse Laplace to determine the system step response (forced response). j) Find the State Space system simulation diagram k) Use Simulink to simulate the system and verify that your analytical solution agrees with the simulation results