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solution05

# solution05 - 1(a The defining differential equation is 2 Rk...

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1/. (a) The defining differential equation is IN SOL S SOL S V mL k x Lm Rk x Lm k m k Lm Rb x m b L R x = + + + + + + & & & & & & 2 Every term in this expression is in m/s 3 . This doesn’t guarantee that it is correct but is a good sign. (b) Plugging in the values given produces 8000 940 20 20 ) ( 2 3 + + + = s s s s H for the given input s s V IN 10 ) ( = therefore j p j p p p p s p s p s p s s s s s s V s H s X IN 5093 . 28 2394 . 5 , 5093 . 28 2394 . 5 , 5212 . 9 , 0 where ) )( )( )( ( 200 ) 8000 940 20 ( ) 20 )( 10 ( ) ( ) ( ) ( 4 2 2 1 4 3 2 1 2 3 = + = = = = + + + = = ° = × = = ° = + = = = = = = + + + = = = = 64 . 86 0042 . 0 10 0042 . 0 0001 . 0 64 . 86 0042 . 0 0042 . 0 0001 . 0 ) ( ) ( 0253 . 0 ) ( ) ( 025 . 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( 3 3 4 3 3 2 2 1 1 4 4 3 3 2 2 1 1 3 2 1 j c c j s X p s c s X p s c s X p s c p s c p s c p s c p s c s X p s p s p s ) 512 . 1 5093 . 28 cos( ) 0042 . 0 ( 2 0253 . 0 025 . 0 ) ( 5 5212 . 9 + + = t e e t x t t Notice that the angle of c 3 has been converted to radians so as to be consistent with 28.5093 t , which is in radians. Mixing up radians and degrees here is a major source of error when student attempt to evaluate expressions like this. Note that, if your calculator is set up to work in degrees, you must instead convert 27.839

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solution05 - 1(a The defining differential equation is 2 Rk...

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