# ae_383_hw1 - a 10 4 = x x x&&& = x 2 = x& b 3...

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AE 383 System Dynamics Homework 1 Handed out: July 5 th , 2007 Due: July12 th , 2007 1) Perform the summation Z 1 + Z 2 = Z for the following complex numbers and check your answers graphically a) Z 1 = 4e ( π /4)j ; Z 2 = 1.0 + j2.0 b) |Z 1 | = 28, Z 1 = 45 o ; |Z 2 | = 16, Z 2 = 135 o 2) Add the two sinusoidal functions ) 8 3 cos( 5 ) ( 1 π + = t t f and ) 4 3 cos( 25 ) ( 2 + = t t f by using Trigonometric method Complex exponential method Matlab 3) Determine the solutions of the following differential equations by using the method of undetermined coefficients
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Unformatted text preview: a) 10 4 = + + x x x & & & , ) ( = x 2 ) ( = x & b) ) 3 sin( t x x = + & & , ) ( = x ) ( = x & For part a) classify the solution as free + forced and transient + steady-state responses 4) Find the Laplace transform of the functions a) f(t) = 0 t < 0 = te-2t t ≥ b) f(t) = 0 t < 0 = 4sin(2t + 30 o ) t ≥ 0 c) 5) Solve the differential equations in Problem (3) by using Laplace Transform technique b a a+b...
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## This note was uploaded on 10/24/2011 for the course AEE 463 taught by Professor Melin during the Spring '11 term at Middle East Technical University.

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