Exam 3 (Version 1) - Solution , Sp'12

A 16 points h2 q b 17 points h3 q c 5 points extra

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Unformatted text preview: a) (16 points) H2/ Q b) (17 points) H3/ Q c) (5 points extra credit) For a unit step change in q2(t) determine q3(t) Tip: The transfer functions of the cascade circuit below is: 2 Sol: (a) ( ) Thus ( ( ) ) ( ) (b) Thus (c) Since () , () () (33 points) 2. Consider the following model: 3 6v 3v g (t ) g (t ) assuming zero initial conditions a. (17 points) Obtain the response of v(t) if g(t) is a unit step function. b. (16 points) Find the time constant and the delay time. c. (5 points extra credit) Obtain the response of v(t) if g (t ) 1 e 5t Sol: (a) Take the Laplace transform: () () () () () () () ( ( ( ) ) ) ( ( ) ) Thus () (b) Compare to the standard form, , where is the time constant The time constant can be derived as Further, the delay time is which time required reaching half the final value. We know ( ) . Thus ( ) 4 Thus (c) () () ( )...
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This note was uploaded on 08/03/2012 for the course IE 474 taught by Professor Srinivasan,c during the Spring '08 term at Purdue University-West Lafayette.

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