2. The following figure shows the left and right endpoints of a linear LC network con- sisting of N identical inductors of inductance L and N + 1 identical capacitors of capacitance C. Let the instantaneous current flowing through the jth inductor be I; (t), for j E {1, . . ., N). a) (20 points) Demonstrate from Kirchhoff's laws that the currents evolve in time according to the coupled equations 1 = wo (lj-1 - 21, + 1;41) , for je {1, . .., N } where wo 1/ VLC and Io = IN+1 = 0 b) (20 points) Find the normal frequencies of the system. I IN-I JN - L L L C C C C