# Pts consider the finite circuit in figure 2 v v v v v

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Problem 5.2 (20 pts) Consider the finite circuit in Figure 2 V V V V V V V 0 1 2 3 4 5 6 Figure 2: Finite circuit All the capacitors have the same capacitance C and all the inductors have the same inductance L . There is no resistance in the circuit. The bottom wire is grounded. 1

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When you apply a harmonically oscillating signal from a signal generator through a coaxial cable to V 6 , different oscillating voltages will be induced along the line. That is if: V 6 ( t ) = V cos( ωt ) then V j ( t ) has the form: V j ( t ) = A j cos( ωt ) + B j sin( ωt ) Find A j and B j . Problem 5.3 (20 pts) Consider a uniform thin string of length L and mass density μ . The string is attached at both ends to vertical, frictionless rods via massless rings as shown in Figure 3. The tension in the string is T . L Figure 3: Uniform String a. Find the normal modes and their frequencies for small amplitude transverse oscillations. b. Sketch the shapes of the first two normal modes. c. Make a graph of the square of angular frequency ω 2 as a function of the angular wave vector k . Problem 5.4 (20 pts) A string of mass density μ and stretched with tension T is deformed as shown in the Figure 4 (amplitude A is very small, the deformation as shown in the figure is greatly exaggerated). The string is released at t
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