10Fall_hw05soln - ECE210 - Fall 2010 - Homework 05...

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Unformatted text preview: ECE210 - Fall 2010 - Homework 05 Solutions 1. Textbook problem 3.15 2. Textbook problem 3.17 1 3. Textbook problem 3.19 2 4. Textbook problem 3.20 (a) 3 The surface is a cone in three dimensions, with its tip at the origin and pointing in the negative z direction. (b) The surface resembles a spiral staircase about the z-axis. 5. Problem 5. (a) For the second-order di erence equation d 2 v dt 2 + 3 dv dt + 2 v = e j 2 t (the same di erence equation as in Prob- lem 3.18 from Homework 4 but with a di erent right hand side), show that the particular solution is v p ( t ) = Ge j 2 t , where G is a complex constant, and solve for G. Solution: v p ( t ) = Ge j 2 t dv p ( t ) dt = j 2 Ge j 2 t d 2 v p ( t ) dt 2 =- 4 Ge j 2 t 4 Substituting these into the di erence equation gives- 4 Ge j 2 t + j 6 Ge j 2 t + 2 Ge j 2 t = e j 2 t Since G is a complex constant, G = + j .- 4 ( + j ) e j 2 t + j 6 ( + j ) e j 2 t + 2 ( + j ) e j 2 t = e j 2 t From this, we have two equations- 4...
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10Fall_hw05soln - ECE210 - Fall 2010 - Homework 05...

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