# hw1 - undetermined coefficients a 1 2 2 = x x x&&&...

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AE 383 System Dynamics Homework 1 Handed out: June 19 th , 2006 Due: June 27 th , 2006 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) Formulate two expressions for f(t) = e σ t cos ω t in terms of complex exponentials. Draw graphically these two ways of representations. 3) Determine the solutions of the following differential equations by using the method of
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Unformatted text preview: undetermined coefficients a) 1 2 2 = + + x x x & & & , ) ( = x 2 ) ( = x & b) ) 3 sin( t x x = + & & , ) ( = x ) ( = x & 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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