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Fall11exam1sol

# Fall11exam1sol - ME-3015 Exam#1 Name(PRINT George W...

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ME-3015 Exam #1 Name (PRINT) 1 George W. Woodruff School of Mechanical Engineering Fall 2011 Solutions Problem 1 (a) (10 points) (b) (10 points) (c) (20 points) (d) (20 points) (e) (20 points) Problem 2 (a) (20 points) (b) (20 points) Problem 3 (a) (20 points) (b) (20 points) Problem 4 (20 points) Problem 5 (20 points) Total (200 points)

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ME-3015 Exam #1 Name (PRINT) 2 1. (80 points) Answer the following short questions. (a) Consider the natural frequency of the two spring-loaded masses shown below. The natural frequency of the vertical system (left) is larger (i.e., faster) than that of the horizontal system (right) due to the gravity. True or False? Briefly explain why. m k mg x m k x Solution : Same natural frequency (gravity does not do anything). The differential equation of motion of the left system with respect to the displacement from the static equilibrium point where the spring force and the gravity force balance does not include a gravity term. (b) Give a transfer function whose poles are at 0, -1, -3 and zeros are at -2 Solution : ) 3 )( 1 ( 2 ) ( + + = s s s s s G (ANS) (c) Obtain the Laplace transformation F(s) of the function below. - - < = b t c b t a a t a b c b t t f ) ( 0 0 ) (
ME-3015 Exam #1 Name (PRINT) 3 a b c t O f ( t ) The definition of Laplace transformation is ) ( ) ( )] ( [ 0 s F dt e t f t f st = = - L . You can use the formula of integration by parts: - = b a b a b a vdu uv udv

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Fall11exam1sol - ME-3015 Exam#1 Name(PRINT George W...

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