C19-activities - ACTIVITY 19-1 F(s) = 6s 14 (s 1)(s 2 + 6s...

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1 ACTIVITY 19-1 2 6s 14 F(s) (s 1)(s 6s 13) −− = −+ + 1 Simple Pole at s 1 2 Complex Conjugate Poles at j α β = −± * 1 AA A Expand: F(s) s1s3j 2 s3j 2 =+ + + + 2 0 3, 13, 13 9 2 αω === = ACTIVITY 19-1 1 2 s1 6s 14 A[ ] (s 6s 13) = = ++ 2 6 (1) 14 20 1 16 ( 1 )1 3 2 0 = == ACTIVITY 19-1 s3 j 2 6s 14 ] (s 1)(s 3 j2) =− + = + 6 ( 3 j2) 14 18 j12 14 ( 3 j2 1)( 3 j2 3 j2) ( 4 j2)( j4) −−+ − − − −+ − −+ + + − + 4j 1 2 ( 8 j16) = (2 j 4 ) x (2j 4 ) (1 j3) 4 ) = 2j 61 2 (4 16) −+ + + = + 10 j10 1 j1 20 2 Rationalization ACTIVITY 19-1 1j 1 / 2 φ + 22 11 2 A + 10 1 tan 45 1 0 2 A/ 4 5 2 ACTIVITY 19-1 1 pt t 1 f(t) A e 2 A e cos( t ) + 1 0 1 A1 ; 3 ; 2 ; 2 p 1; A / 45 2 =− = = t3 t o f(t) 1e 2 e cos(2t 45 ) t 0 => = − + + t e is a Growing Exponential Unstable => ACTIVITY 19-2 2 6s 38 6s 38 a) F(s) ss6( s2 ) ( ) + + 12 Simple, Real Poles at s 2, s 3 Expand: F(s) s2s3 = >= = => = +
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2 ACTIVITY 19-2a 1 s2 12 38 A( ) F ( s ) 1 0 23 = −− =− = = + 2 s3 18 38 s 3 ) F ( s ) 4 32 =+ = = 2t 3t f(t) 10e 4e t 0 => = − + ACTIVITY 19-2 2 2 20s 179s 125 b) F(s) s (s 6s 25) ++ = * 1 AA A Expand: F(s) ss 3 j 4s 3 j 4 + +− 22 2 00 1 Simple, Real Pole at s 0 3; 25; 4 Complex Conjugate Poles at s 3 j4 αω
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C19-activities - ACTIVITY 19-1 F(s) = 6s 14 (s 1)(s 2 + 6s...

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