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Unformatted text preview: Solutions for Test 3, 09 1 Problem form. vector matrix in , , Get sketches. w/ Show a) V T W W nc nc force. 1 dashpots, 2 springs, 2 masses, 2 with system 2DOF ) ( 1 2 x x c  2 x c ) ( t F 2 x 1 x [ ] [ ] ) ( ) ( ) ( ) ( ) ( 2 1 2 1 1 1 1 2 1 2 2 2 1 2 1 1 1 2 1 x Q x C x x c c c c c t F x x x x c x x c t F x x x c W T nc = + = + = Solutions for Test 3, 09 1 Problem form. vector matrix in , , Get sketches. w/ Show a) V T W W nc nc force. 1 dashpots, 2 springs, 2 masses, 2 with system 2DOF [ ] x x M x x m m x x x m x m T T 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2 2 1 1 = = + = [ ] x x K x x k k k k k x x x x k x k V T 2 1 2 1 ) ( 2 1 2 1 2 1 2 2 2 2 1 2 1 2 1 2 2 2 1 1 =  + = + = =  + + + + = + + ) ( 2 1 2 2 2 2 1 2 1 2 1 1 1 1 2 1 2 1 t F x x k k k k k x x c c c c c x x m m K C M ) ( form. vector matrix in EOMs Get b) Q x x x Solutions for Test 3, 09 2 Problem modes. the Describe modes. and s frequencie natural Find a) = + + 2 2 4 2 x k x m mr mr mr I : EOMs with system 2DOF [ ] mI mr I k mr I k mI mr I k r m mr I m r m m k mr I m k mr mr mr I M K ) 4 ( , ) 4 ( ) 4 ( 4 ) 4 ( 4 ) ( ) 4 ( 2 2 ) 4 ( ) det( 2 2 2 2 4 2 2 4 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 + = + = + + = + = + = Solutions for Test 3, 09 2 Problem modes. the Describe modes. and s frequencie natural Find a) = + + 2 2 4 2 x k x m mr mr mr I : EOMs with system 2DOF = = = 1 : 1 1 2 1 x x k + = =  + + + + = 2 2 2 2 2 2 2 2 2 2 2 4 2 4 ) 4 ( 2 ) 4 ( 2 ) 4 ( : ) 4 ( mr I mr x x I kmr I mr I rk I mr I rk mI mr I k mI mr I k Solutions for Test 3, 09 2 Problem . , of terms in about momentum angular system Find b) 2 1 C = + + 2 2 4 2 x k x m mr mr mr I : EOMs with system 2DOF ( 29 [ ] k k r r H 2 ) 4 ( ) 2 ( ) 2 ( 2 x mr mr I x r m r I m...
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