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Unformatted text preview: ECE 2704: MIDTERM EXAM 2 Name: _______________________________SOLUTION_____________________ Signature:__________________________________________________________ NOTES: 1. Two hand‐written 8.5x11 sheets of paper are permitted. It must be your own handwriting. Electronic printing and photocopying is strictly prohibited. 2. Scores are based on correctness and clarity of presentation. 3. No calculators are allowed. 4. You may use Tables 4.1 and 4.2 5. The exam will end promptly at 2:15 pm. 6. Put a box around your answers. 1. Suppose , and let Starting with the definition of the Laplace transform, compute that the Laplace transform of and the region of convergence. DO NOT use the tables, and DO show all your work. Solution There is no restriction on required to evaluate the integral, so the region of convergence is the entire complex plane. 2. An impulse is applied to a system with zero initial conditions, and the corresponding output is measured and found to be . Find the transfer function for this system. Solution . Since , this is the transfer function. 3. Using the Laplace transform, compute the solution to the ordinary differential equation where and Solution Implies that Thus Partial fraction expansion yields and the solution is 4. Find the single transfer function that represents the block diagram below where , , and are transfer functions. + X + Σ
- G + Σ F Y H Solution + + Σ
- G + Σ W F H Label the node shown above as . Then and Noting that , 5. For what values of the real‐valued scalar is the system below stable? X + Σ
- 1 S‐1 k Y Solution The transfer function of the system is . The system is stable for ...
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This note was uploaded on 02/07/2011 for the course ECE 2704 taught by Professor Djstilwell during the Fall '08 term at Virginia Tech.
- Fall '08