Exam1_Fall05

# Exam1_Fall05 - MEEN 364 FALL 2005 Texas A&M University...

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MEEN 364 FALL 2005 Page 1 of 11 Texas A&M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls EXAM 1 – Oct 5, 2005 @ 7 PM – 9 PM, ZACH 102 NO CALCULATORS ARE ALLOWED CLOSED BOOKS AND CLOSED NOTES N a m e : Please circle your section below: Section (Lab Time): 501(M 1:50-4:40 PM) 502(T 8:00-10:50 AM) 503(T 2:20-5:10 PM) 504(W 1:50-4:40 PM) 505(R 11:10-2:00 PM) 506(R 2:20-5:10 PM) Problem 1 [30 points] a) Compute the Laplace Transforms of the following functions, which are defined only for 0 > t . ) ( cos 3 ) ( sin ) ( 2 2 t t t f + = . ( Hint: ) ( sin ) ( cos ) 2 cos( 2 2 t t t = ) ) cos( 2 ) ( t t te t g t + = . ( Hint : [] ) ( ) ( s H ds d t th L = ) b) Compute the time function corresponding to the following Laplace Transform: 2 2 ) 1 ( ) 1 ( 2 ) ( + + + = s s s s s F c) Compute the Fourier series expansion of the following function: ) sin( ) cos( ) ( t j t t f + = d) The Fourier transform of a discrete signal x(n) , is given by: −∞ = = n n j e n x X ω ) ( ) (. What is the Fourier transform of, ) ( 0 n x e n j in terms of X( ω ) ?

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Exam1_Fall05 - MEEN 364 FALL 2005 Texas A&M University...

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