fin_sample_soln

# fin_sample_soln - ( s ) = s ( C ( R 1 + R 2 ) s + 1 + 10 6...

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2.003 Fall 2002 Final - Sample problems - Answers Problem 1 To solve this problem it is easiest if you use the initial and Fnal value theorems. ±inal Value theorem: lim lim f ( t ) = sF ( s ) t s 0 Initial Value theorem: lim f (0 + ) = sF ( s ) s 1 , c, j 2 , h, o 3 , f, i 4 , d, k 5 , a, m 6 , g, p 7 , e, l 8 , b, n Problem 2 1. v 1 (0 ) = 1, v 1 (0 ) = 1, x (0 ) = 1 m 2. x (0 + ) = 1 m, ˙ x (0 + ) = 1 m/s 3. k x ˙ + x = 0 b 2 4. k t x ( t ) = e b 2 Problem - 3 1. a ( s )( CR 2 s + 1) R 2 1 C ( s ) = ± − Cs ( R 1 + R 2 ) + 1 + a ( s ) CR 1 s R 1 CR 1 s 2. Proportional and Integral, K p = R 2 /R 1 , K i = 1 / ( CR 1 ) 3. 10 6 ( CR 2 s + 1) C

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Unformatted text preview: ( s ) = s ( C ( R 1 + R 2 ) s + 1 + 10 6 CR 1 ) 1 2.003 F all 2002 F inal - S ample pr oblems - A nswer s Bode Diagram i 0 0 Phase (deg) Magn tude (dB) -10 10 20 30 40 50 -90 -45 1 2 3 4 5 6 10 10 10 10 10 10 10 Frequency (rad/sec)...
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## This note was uploaded on 02/23/2012 for the course MECHANICAL 2.003 taught by Professor Davidtrumper during the Spring '05 term at MIT.

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fin_sample_soln - ( s ) = s ( C ( R 1 + R 2 ) s + 1 + 10 6...

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