ASE 365 - Lecture 9 - Response to periodic inputs...

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Unformatted text preview: Response to periodic inputs Cam-follower example: k 1 c m x(t ) k 2 0 y(t ) FB D fD fS 1 fS 2 m ) ( 2 1 2 1 y x k x c x k f f f x m S D S---- =- + = ) ( ) ( ) ( 2 2 2 1 T t y k t y k x k k x c x m + = = + + + : EOM y(t ) t T s. ' and s ' the of ity orthogonal of because found be can series Fourier the in s ' and s ' The where general, In sin cos 2 ), sin cos ( 2 ) ( ) ( ) ( ) ( 1 p p p p p b a T t p b t p a a t f T t kf t kf t F kx x c x m = + + = + = = = + + = Orthogonality of basis functions = = = + + + -- + + + =- + + = + + + + + + q p T q p q p t q p t q p q p q p t q p q p t q p dt t q p t q p dt t q t p T t t T t t T t t T t t T t t T t t if if if if , 2 , , ] [ 2 1 ) ( ) sin( 2 1 , ) ( ) sin( 2 1 ) ( ) sin( 2 1 ) cos( ) cos( 2 1 cos cos = = + +- -- = +-- = + + + + q p T q p q p q p t q p q p t q p dt t q p t q p dt t q t p T t t T t t T t t T t t if if (if , 2 , ) ) ( ) sin( 2 1 ) ( ) sin( 2 1 ) cos( ) cos( 2 1 sin sin q p q p q p q p t q p q p t q p dt t q p t q p dt t q t p T t t T t t T t t T t t = = --- + + +- =- + + = + + + + if or if (if , ) ) ( ) cos( 2 1 ) ( ) cos( 2 1 ) sin( ) sin( 2 1 cos sin Multiply f(t) by cos q0t and integrate over one period: Similarly, multiply f(t) by sin q0t and integrate: , 2 , 1 , , cos ) ( 2 2 cos ) sin cos ( 2 cos ) ( 1 = = = + + = + + = + q dt t q t f T a T a dt t q t p b t p a a dt t q t f T t t q q T t t p p p T t t , 3 , 2 , 1 , sin ) ( 2 2 sin ) sin cos ( 2 sin ) ( 1 = = = + + = + + = + q dt...
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This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

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ASE 365 - Lecture 9 - Response to periodic inputs...

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