An LC circuit can be modeled by the following system of differential equations: di, 1 (i-i2)...

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An LC circuit can be modeled by the following system of differential equations: d²i, 1 (i-i2) = 0 dt C d'iz L2 dt2 1 i3)- (i - i2) = 0 C1 C2 d?iz L3 dt2 C3 1 (iz - i3) = 0 Where L=inductance (H), 1-time(s), i=current (A), and C=capacitance (F). Assuming that a solution is of the form i, = 1 sin(wt), determine the eigenvalues and eigenvectors for this system with L; =1 H and C,=1 F. Calculate the natural circular frequency of the system, o. An LC circuit can be modeled by the following system of differential equations: d²i, 1 (i-i2) = 0 dt C d'iz L2 dt2 1 i3)- (i - i2) = 0 C1 C2 d?iz L3 dt2 C3 1 (iz - i3) = 0 Where L=inductance (H), 1-time(s), i=current (A), and C=capacitance (F). Assuming that a solution is of the form i, = 1 sin(wt), determine the eigenvalues and eigenvectors for this system with L; =1 H and C,=1 F. Calculate the natural circular frequency of the system, o.