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# A#16 - X 1 s X 4(10 Solve the following differential...

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Assignment #16 ECSE-2410 Signals & Systems - Spring 2007 Tue 04/3/07 1(30). Find the inverse Laplace transform of (a)(10). 1) + s + s ( 2) + (s 3 + s = (s) X 2 a . Express your answer in the form . ) ( cos t u Be u(t) ) + t ( e A t t - β α θω + (b)(10). 3 + 2s + s 0.5 + s = (s) X 2 b . Express your answer in the form . u(t) ) + t ( e C t - φω γ sin (c)(10). () ( ) 2 2 + s + s s = (s) X c , where is an unknown parameter. 2(16). Find the initial and final values for the signals below. (a)(8). Find the initial and final values of x a ( t ), where s e s X s a + = 1 1 ) ( 2 . (b)(8). Find the initial and final values of x b ( t ), where ) 4 + s ( s 1 + 2s - s = (s) X 2 2 b . 3(12). (a)(4). Find the Laplace transform of the signal, . else 0 2 t < 0 t = (t) x , , 1 (b)(8). Now suppose signal is made up of signal repeated every two seconds starting at ) ( 2 t x ) ( 1 t x 2 = t . Find the Laplace transform, of this repeating waveform in terms of from part (a). Express your answer in closed form. ) ( 2 s

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Unformatted text preview: X ) ( 1 s X 4(10). Solve the following differential equation using Laplace transforms. 1 ) ( , 1 ) ( ), ( 2 ) ( 2 ) ( 2 ) ( 2 2 = = = + + − − dt dy y t x t y dt t dy dt t y d , where the input, , is a unit step, . ) ( t x ) ( t u Assign#16. p.1 5(32). The following pole-zero diagrams represent the system transfer function, H ( s ). In each case find (a) the damping factor (or damping ratio), ζ , the (b) natural frequency, ω n , the (c) damped frequency, 2 1 ζω − = n d , and (d) sketch qualitatively the step response, s ( t ). (You can use MATLAB to check your answers here, but are not required to do so.) j 6-j 6 j 4 -j 4 -1 -8-1-j 4 j 4-9 j 2 -j 2 -3 s-plane s-plane s-plane s-plane A B C D Assign#16. p.2...
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A#16 - X 1 s X 4(10 Solve the following differential...

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