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midS11sol

# midS11sol - Name ME 475 MIDTERM EXAMINATION Spring 2011...

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Name _______________________________ ME 475 MIDTERM EXAMINATION Spring 2011 March 1, 2010 8-10 pm ARMS 1010 Problem 1 /20 Problem 2 /20 Problem 3 /20 Problem 4 /20 Problem 5 /20 TOTAL /100 INSTRUCTIONS: This is a Closed book exam. You are permitted one 8 1/2 × 11 help sheet of your own design. You have two hours to complete the exam. Label and circle your answers.

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2 Laplace Transform Pairs f(t) F(s) Comment 1. u i (t) 1 Unit impulse 2. u s (t) 1 s Unit step 3. u r (t) 2 1 s Unit ramp 4. e at - 1 s a Exponential 5. sin ϖ t ϖ ϖ s 2 2 Sine 6. cos ϖ t s s 2 2 ϖ Cosine 7. f(t) F(s) Function 8. df t dt ( ) sF(s) - f(0) First Derivative 9. d f t dt n ( ) s F s s f s df dt n n n ( ) ( ) ( ) - - - - 1 2 0 0 n th Derivative 10. t n n s n ! + 1 11. e f t at - ( ) F s a ( ) 12. te at - 1 2 ( ) s a + 13. t e n at - n s a n ! ( ) + + 1 14. e t at - sin ϖ ϖ ϖ ( ) s a + + 2 2 15. e t at - cos ϖ ( ) ( ) s a s a + + ϖ 2 16. Initial Value Theorem : f (0 + ) = lim s → ∞ sF ( s ) 17. Final Value Theorem : lim ( ) lim ( ) t f t s sF s → ∞ = 0
3 Problem 1 : (20 points) (a) Determine the desired second-order root locations that would satisfy the following specifications: (i) damped natural frequency of 5 rad/sec.

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midS11sol - Name ME 475 MIDTERM EXAMINATION Spring 2011...

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