Hmw10 - X 1 s = s 10 s 2 8 s 18 X 2 s = 1-e-2 s s 4 X 3 s = 1 s s 1 2 4 ±ind the initial and ²nal values(if they exist of the signals with

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Due Apr 14, 2010 BME 171, Spring 2010 - HOMEWORK #10 Laplace Transform 1. Obtain the Laplace transform of the triangular signal x ( t ) = Λ( t - 1) by using the diFerentiation theorem, time-delay theorem, and expressing dx/dt in terms of unit step functions. 2. A signal has the Laplace transform X ( s ) = s + 2 s 2 + 4 s + 5 ±ind Laplace transforms, X i ( s ) , i = 1 , ... 5, of the signals listed below. In each case, specify which properties you are using. x 1 ( t ) = x (2 t - 1) u (2 t - 1) x 2 ( t ) = e - 3 t x ( t ) x 3 ( t ) = x ( t ) * x ( t ) x 4 ( t ) = dx/dt x 5 ( t ) = x ( t ) cos(7 t ) 3. ±ind the inverse Laplace transforms of the functions of s given below.
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Unformatted text preview: X 1 ( s ) = s + 10 s 2 + 8 s + 18 X 2 ( s ) = 1-e-2 s s + 4 X 3 ( s ) = 1 s ( s + 1) 2 4. ±ind the initial and ²nal values (if they exist) of the signals with Laplace transforms given below. Y 1 ( s ) = s + 10 s 2 + 3 s + 7 Y 2 ( s ) = s 2 + 5 s + 7 s 2 + 3 s + 7 5. An LTI system is given by an ODE: d 2 y dt 2 + 6 dy dt + 5 y ( t ) = x ( t ) . (a) ±ind the transfer function H ( s ) of this system. (b) ±ind the response of this system to input x ( t ) = e-7 t u ( t )....
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This note was uploaded on 05/25/2010 for the course BME 171 taught by Professor Izatt during the Spring '08 term at Duke.

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