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Unformatted text preview: B. Balachandran ENME361 Vibrations Fall 2008 Solution to Quiz #2 (September 11, 2008; Duration: 10 minutes) 1) Consider the differential equation 2 2 ( ) ( ) 2 ( ) ( ) d w t dw t w t u t dt dt + + = where is a constant such that 0 < < 1 and u ( t ) is the unit step function. Given that the initial conditions are zero; that is, w (0) = dw (0)/ dt = 0, solve for the solution w ( t ) by using the Laplace transform technique. Some Laplace transform pairs are provided at the end. Taking Laplace transforms of the different terms on both sides, the differential equation is transformed into the algebraic equation s s w w s sW w sw s W s 1 ) ( )) ( ) ( ( 2 ) ( ) ( ) ( 2 = + + where L [ w ( t )] = W ( s ), the prime is used to indicate a time derivative, and we have made use of the table for the Laplace transform of the unit step function with t o = 0. Applying the initial conditions ) ( ) ( = = w w and solving for W ( s ), we arrive at ) 1 2 ( 1 ) ( 2 + + = s s s...
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This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.
- Spring '11