Exam1_Fall02

# Exam1_Fall02 - MEEN 364 Exam 1 Texas A&M University...

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MEEN 364 Exam 1 1 Texas A&M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls EXAM 1 – October 9, 2002 7:15 – 9:15 PM; Room 110 Harrington Name: 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 AM – 2:00 PM) 506(R 2:20-5:10 PM) 1) a) [10 points] Obtain the Laplace transform of the following function. . 0 ); sin( 1 ) ( + = t t t t f [ Hint: [] ). ( ) ( s F ds d t tf L = ] b) [15 points] The governing differential equations of motion for a system is given by , 6 ) ( 4 ) ( 4 ) ( . .. t e t y t y t y = + + for 0 t . Solve the differential equation for the initial conditions given by . 2 ) 0 ( and 1 ) 0 ( . = = y y Determine whether the response of the system reaches a steady state value? If yes, what is the steady state value? 2) Consider the following continuous-time signal ). 2000 sin( 5 ) 10000 sin( 7 ) 8000 cos( 6 ) 5000 cos( 8 ) ( t t t t t x a π + + + = a) [7 points] What are the frequencies present in the signal ) ( t x a and what is the range of sampling rates required to avoid aliasing effects?

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Exam1_Fall02 - MEEN 364 Exam 1 Texas A&M University...

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