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SignalsHW15S07

# SignalsHW15S07 - = 1 what is the steady-state output y t of...

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Assignment #15 ECSE-2410 Signals & Systems - Spring 2007 Fri 03/30/07 1(28). Find the Laplace transform of (a)(8) . else 0 3 < t < 1 1 = (t) x a (b)(10) . 3) - u(t e = (t) x 2) - -(t b (c)(10) . u(t) ) 45 + t ( e 5 = (t) x t -2 c ° π cos 2(30). Find the inverse Laplace transform for the signals below. Note. You must use properties. No integration is possible. (a) (10) Find x a ( t ) , the inverse Laplace transform of s e s X s a + = 1 1 ) ( 2 . (b) (10) Find x b ( t ), the inverse Laplace transform of ) 4 + s ( s 1 + 2s - s = (s) X 2 2 b . (c) (10) Find x c ( t ) , the inverse Laplace transform of = (s) X c 6 5 4 + s + s e s 2 s . 3(15). Given the transfer function, s) + ( s + s 10 = H(s) 1 ) 16 ( 2 + , find the impulse response. 4(15). A second-order system is described by the differential equation ) ( ) ( ) ( 2 ) ( 2 2 t x t y dt t dy dt t y d K = + + , where K is a constant. (a) (5 pts) Find the value of K that will make the system critically damped. (b) (5 pts) If K = 4, find the impulse response, ( ) t h , for this system. (c) (5 pts) If K

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