4hw4 - Physics 315 Oscillations and Waves Homework 4 Due in...

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Physics 315: Oscillations and Waves Homework 4: Due in class on Wednesday, Sept. 30th 1. The fgure below shows the leFt and right extremities oF a linear LC network consisting oF N identical inductors oF inductance L , and N + 1 identical capacitors oF capacitance C . Let the instantaneous current ±owing through the i th inductor be I i ( t ), For i = 1 , N . Demonstrate From Kircho²’s circuital laws that the currents evolve in time according to the coupled equations ¨ I i = ω 2 0 ( I i - 1 - 2 I i + I i +1 ) , For i = 1 , N , where ω 0 = 1 / L C , and I 0 = I N +1 = 0. ³ind the normal Frequencies oF the system. . I 2 C L L L I N I N - 1 I 1 L C C C 2. Suppose that the outermost two capacitors in the circuit considered in the previous exercise are short-circuited. ³ind the new normal Frequencies oF the system. 3. The linear LC circuit considered in Question 1 can be thought oF as a discrete model oF a uniForm lossless transmission line: e.g. , a co-axial cable. In this interpretation,
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4hw4 - Physics 315 Oscillations and Waves Homework 4 Due in...

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