Review Problems

Review Problems - Lehigh University Department of...

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Lehigh University Department of Mechanical Engineering and Mechanics ME 242 Mechanical Engineering Systems FINAL EXAM REVIEW PROBLEMS Start by reviewing the solution to Example 6.3 page 398 and 399. Essentially you will be getting the same solution utilizing Laplace transform methods and partial fraction expansions. 1. Find the Laplace Transform of ( ) 2 2 2 5 d x dx x u t dt dt + + = subject to an arbitrary input and arbitrary initial conditions ( ) 0 x and ( ) 0 x d . Solve for ( ) X s in terms of the arbitrary input and initial conditions. 2. If ( ) 0 u t = , ( ) 0 .6 x = - and ( ) 0 1 x = d , what is the total time solution for ( ) x t ? 3. What is the response of x to a unit step in ( ) u t ? (This is the step response, ( ) h t .) 4. What is the response of x to a unit impulse in ( ) u t ? (This is the impulse response, ( ) g t .) This solution can and should be found in two alternative ways, by taking the inverse Laplace transform of ( ) G s and by taking the time derivative of the solution
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Review Problems - Lehigh University Department of...

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