fall 2004 EE 3120 test #2

# fall 2004 EE 3120 test #2 - b From this plot talk about the...

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Name:_____________________________________ EE 3120 Test # 2 SSN:_______________________________________ Fall 2004 1. Given X(s), find x ( t ) using the Laplace transform table. 2 2 4 5 ( ) ( 1) s s X s s s + - = - 2. Given H(s), find the differential equation for the system. H(s) = 2 3 2 3 6 2 5 7 s s s s s + - - + +

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3. Some Laplace transform tables have additional transforms. Your table is missing transforms for the time domain function cos o t t ϖ and sin o t t . Derive the Laplace transform of cos o t t using the Laplace transform table and Laplace transform properties table. You DO NOT need to find this transform using the Laplace transform integral.
4. The Matlab residue function is applied to a transfer function H(s) with the following results. r = -1.2500 + 0.2500i -1.2500 - 0.2500i 0.5000 p = -1.0000 + 1.0000i -1.0000 - 1.0000i 0 k = 1 a. Plot the poles in the complex s-plane.

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Unformatted text preview: b. From this plot talk about the stability of the transfer function. c. Find the impulse response h ( t ). 5. The unit step response of a system is given by: 2 ( ) (4 4 ) ( ) t y t e u t-=-. a. Find the impulse response h ( t ) without using any transforms. b. Find the impulse response h ( t ) using the laplace transform. 6. Using the table, find the convolution of x ( t) and h ( t ). 4 ( ) 5 cos(2 .67) ( ) ( ) ( ) t h t e t u t x t u t-= + = 7. Find the convolution graphically of x ( t) and h ( t ): ( ) ( ) ( ) ( 1) 2 ( 2) ( 3) x t u t h t u t u t u t = =---+-8. Consider the circuit shown below. Find the transfer function. Find the output v ( t ) excited by a 2 V DC input voltage source and the initial conditions i (0-)= -1 A, and v (0-) = -2 V....
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fall 2004 EE 3120 test #2 - b From this plot talk about the...

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