1. In the mechanical system shown below all elements are assumed to be linear except the frictional damper that exerts a nonlinear force FNLD on mass m2. The nonlinear damping force is given by The angular displacement FNLD = 2+3v2+3 V2 V2 of the bar with mass my attached to it is very small. The parameters of the system were selected so that the bar is in a horizontal position, 6 = 0, when the external force F; = 0.| L/2 k C FNLD m2 MILO KLO - L/2 mi massless bar k 44 X2 v2(t) Fi(t) =O M2X2 + FNLD (12) + Kx2. - KLO = Fi(t) 1) Derive the nonlinear state variable model in terms of state variables 0, 2, x2, V2. 2) Find the values of normal operating point (static equilibrium point) for all state variables when Fi F =12 N, using the following values of the system parameters: K 100 N/m L = 2m Calculate the incremental damping constant, binc dF NLD . Linearize the = dv2 v2=2=0 state-variable equations and derive a linear state-variable model in terms of the incremental state variables Ô,Ô, ✰₂, ₂.