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ASE 365 - Practice Test 2

# ASE 365 - Practice Test 2 - ASE 365Structural Dynamics Dr J...

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ASE 365—Structural Dynamics Name: Dr. J. K. Bennighof April 2, 2009 TEST 2 This test is closed-book, except that you are allowed to use one two-sided sheet of notes that you have prepared beforehand. Do all of your work neatly , with each problem beginning on a separate page. Clearly designate each of your answers with a box or circle. When you hand in your test, place the test handout, with your name on it, on top, followed by your work, with your sheet of notes on the bottom. Staple all pages together. Problem 1 (25%) An undamped single degree of freedom system is excited by a delayed step input so that it has the equation of motion m ¨ x + kx = F ( t ) = F 0 U ( t - T ) = braceleftbigg 0 , t < T F 0 , t T where U ( t ) is the unit step function. (a) Consider the response over the two time intervals 0 t T and t T , and explain why x ( t ) = integraldisplay t 0 F ( τ ) g ( t - τ ) becomes x ( t ) = U ( t - T ) integraldisplay t T F ( τ ) g ( t - τ ) for this problem.

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