Problem 5. Consider the nonlinear circuit below. The voltage across the capacitor, vc and the current through the inductor, iL, have the following dynamicsv̇ċ = -10 vc - 10 vc^3 10 iL 10 vi(diL)/(dt) = -5 vc 5 viwhere vi is the input voltage to this circuit. Define the state variables of the system as x1 = vc and x2 = iL.a) Find a nonlinear state-space equation that describes the system.b) Linearize the system around x0 = = , and u0 = 1. write down the linear state-space equationc
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