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In this problem, you will linearize the dynamics of the magnetic levitation device shown below. An electro-magnet is used to suspend a metal ball in the air. The nonlinear dynamics of the ball are my(t)=mg202N2Ay(t)2u(t)2 where m is the mass of the ball, g is the gravitational constant, and ,0,N, and A are physical parameters related to the electro-magnet. The input u(t) is the current through the magnetic coil and the output y(t) is the position of the ball. a) Find the equilibrium current u, velocity y, and acceleration y needed to hold the ball at an equilibrium distance of y=2. b) Linearize the dynamics about this equilibrium. c) Find the transfer function for the linearized dynamics. Is the transfer function stable for y>0