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20095ee102_1_EE102_Hw3

# 20095ee102_1_EE102_Hw3 - 2 = = x x 3 For the given circuit...

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Fall 2009 EE102 HW #3 Due October 21 1. Find the Laplace transforms of the following functions: a) t e t t x 3 2 ) ( = 0 , t b) ) cos( ) ( wt t x = 0 , t 2. Using Laplace transform for the given differential equation: ) ( ) ( 4 ) ( 2 2 t u t x t x dt d = + a) Find the Transfer function and its inverse transform. b) Assume u(t) = 0, and find the zero-input response c) Now assume the input u(t) is the unit step response: 0 , 1 ) ( = t t u Find the output x(t) given the following initial conditions:
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Unformatted text preview: ) ( , 2 ) ( ' = = x x 3. For the given circuit below, The input is u(t) and output is v(t) (voltage across the capacitor). R = 400 Ω, L = 100 H, C = 5 mF a) Find the input-output relation as a differential equation. b) Find the Transfer function and its inverse transform. c) Calculate the gain and phase of the Transfer function....
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