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Practice Final

# Practice Final - Name Department of Mechanical Engineering...

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Name_________________________ Page 1 of 11 12/8/2005 Name ____________________________________ Department of Mechanical Engineering and Mechanics Lehigh University ME 242 Mechanical Engineering Systems Practice Final Exam May 01, 2003 Points total 100---problems are not weighted equally. No books or notes allowed 2 4 2 2 0 8 ; ; ; 2 d L A L P P Q C I a c A g A μ ρ ρ π ρ = = = = Time function, 0 t Laplace Transform 1 ( ) a f t ( ) a F s 2 ( ) ( ) a f t b g t + ( ) ( ) a F s b G s + 3 ( ) n n d f t dt ( ) ( ) ( ) 1 1 2 1 0 0 0 n n n n n t d f s F s s f s f dt - - - - = - - - - dotnosp 4 ( ) t f t dt -∞ ( ) ( ) 0 1 F s f t dt s -∞ + 5 ( ) tf t ( ) dF s ds - 6 ( ) at e f t - ( ) F s a + 7 Unit impulse, ( ) t δ 1 8 1 ! n at t e n - , 0,1,2, n = ( ) 1 1 n s a + + 9 ( ) f t T - ( ) Ts e F s - 10 sin at e t ω - ( ) 2 2 s a ω ω + + 11 cos at e t ω - ( ) 2 2 s a s a ω + + + 12 ( ) ( ) 2 cos sin r p t r i i i e r p t r p t - ( ) ( ) 2 2 2 2 r i r i r i r i r r i i r i r r j r r j s p p j s p p j r s p r p s p p + - + - - - + - - = - + Fourier Series; ( ) ( ) ( ) 0 0 0 1 2 cos 2 sin n n n f t a a n t b n t ω ω = = + + where ( ) /2 / 2 1 2 cos T n T nt a f t dt T T π - = , ( ) /2 / 2 1 2 sin T n T nt b f t dt T T π - = , 0 2 T π ω = .

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Name_________________________ Page 2 of 11 12/8/2005 1. (Fall 2000 ) A system is modeled by the differential equations 3 6 dp q dt = - 3 3 dq q p dt = - - Determine the values and the names of whichever of the following parameters that apply: n ω , d ω , ς , τ .
Name_________________________ Page 3 of 11 12/8/2005 2. (Spring 2001) Define state variables and write differential equations for the following model shown in bond graph form. The moduli of elements are constant except for the resistance which can be expressed as either R R e aq = dotnosp or 2 R R q ae = dotnosp a. Is the bond graph reducible to a tree like structure? Yes or No (please circle) b. Assign causality to all bonds. c. Is the system causal, under causal or over-causal (circle your answer)?

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Practice Final - Name Department of Mechanical Engineering...

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