The electric circuit shown in Figure 7.6.7 is described by
Chapter 7, Problem 26(choose chapter or problem)
The electric circuit shown in Figure 7.6.7 is described by the system of differential equationsddt IV=01L 1C 1RCIVwhere I is the current through the inductor and V is the voltage drop across the capacitor.These differential equations were derived in of Section 7.1.(a) Show that the eigenvalues of the coefficient matrix are real and different if L > 4R2C;show that they are complex conjugates if L < 4R2C.(b) Suppose that R = 1 , C = 12 F, and L = 1 H. Find the general solution of thesystem (i) in this case.(c) Find I(t) and V(t) if I(0) = 2 A and V(0) = 1 V.(d) For the circuit of part (b) determine the limiting values of I(t) and V(t) as t . Dothese limiting values depend on the initial conditions?
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