# Hwk7f06 - t = 0 s (S2 remains open). (a) Determine y ( t )...

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ECE 3337 Homework 7 Fall 2006 Due: November 29 (Jansen), 30 (Kalatsky), 2006 1. Find the Laplace transform of: (a) cos(6 πt - π/ 3) u ( t ) (b) x ( t )= ± t 1 t 2 0 elsewhere 2. Find the signal for which the single-sided Laplace transform is: (a) X ( s )= 2 s +10 s ( s + 10) (b) X ( s )= 2 s +20 ( s - j )( s + 10) 2 (c) X ( s )= 1 - e - 2 s s 2 +2 s +10 3. Solve using the Laplace transform: y ±± ( t )+6 y ± ( t )+5 y ( t )= r ( t ) with y (0) = 0, y ± (0) = 3, and r ( t ) = 3 cos(6 πt - π/ 3) u ( t ). 4. Find the Laplace transforms of the periodic function whose de±nition in one period is f ( t )= t for 0 t<π and f ( t )= π - t for π t< 2 π . 5. Assume that S1 and S2 of the circuit presented in Figure 1 have been open for a long time, and that S1 closes at

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Unformatted text preview: t = 0 s (S2 remains open). (a) Determine y ( t ) when x ( t ) = δ ( t ). (b) Determine y ( t ) when x ( t ) = u ( t ). (c) Determine a set of values for R, L and C such that the system works as a bandpass-±lter with a center frequency at 750 kHz. Please set realistic values for L and C, i.e., the order of magnitude should be milli Henrys, and micro Farads, respectively. (d) Now assume that S1 opens again, and that S2 closes at t = 10 s . What would be the system’s output for problem 5b? 1 Figure 1: Circuit for problem 5. 2...
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## This note was uploaded on 10/26/2011 for the course ECE 3337 taught by Professor Staff during the Fall '08 term at University of Houston.

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Hwk7f06 - t = 0 s (S2 remains open). (a) Determine y ( t )...

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