Compare with the results obtained in problem set 2

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amplitudes of three oscillating masses the three normal modes. Compare with the results obtained in Problem Set #2, problem 2.5. Notice that you DO NOT have to solve any third order polynomials or use any computer beyond the simple calculator with trigonometric functions. Problem 4.2 (20 pts) L L L C C C C L L L C C C I j I j+1 I j-1 Figure 2: Infinite LC chain. Consider the infinite chain of inductors and capacitors (transmission line) as shown in Figure 2. Assume that the distance between two inductors is a . a. Write the differential equations for the currents in the inductors as a function of position along the chain j . How many ”‘neighbors”’ are affecting the current in inductor j ? b. Assume that there are normal modes with currents of given by I ( j ) = e ijka . Find the dispersion relation ω 2 = f ( k ) for these modes. c. Construct a finite chain by removing inductors at j = 0 and j = N + 1. Find the normal modes shapes and frequencies for such a chain. 2
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  • Spring '14
  • Boundary value problem, Massachusetts Institute of Technology, Normal mode, normal modes, independent normal modes

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