HW1a - AE 383 System Dynamics Homework #1 Due: Oct. 30,...

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AE 383 System Dynamics Homework #1 Due: Oct. 30, 2006 1. Identify the types of the mathematical models given below: a. 2 2( ) () x tx y f t yt x g t ++ = += ±± ± ± b. 2 2 sin( ) ( , , ) uu u tp x y t xy t ∂∂ = c. 11 1 2t a n ( ) kk k k x kTx yy y xk T +− + =+ d. 22 3 ( ) u u f t + ± 2. Find the Laplace transformation of the following time functions: a. sin(2 ) 0 03 / 2 tt ft t π = b. cos(5 ) 0 /5 2 /5 4 /5 04 / 5 t gt t t t ππ +≤ =− + ≤≤ > 3. Solve the following o.d.e.’s using Laplace transformation and inverse Laplace transformation. a. 54s i n ( 3 ) 2 ;( 0 )( 0 ) 0 yyy t t y y ++= + = = ± ± b. 3 ( ) ; (0) 1, (0) 2, (0) 3 zz u t z z z =
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HW1a - AE 383 System Dynamics Homework #1 Due: Oct. 30,...

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