equationsheetfull_SP10

# equationsheetfull_SP10 - ME 365 EQUATIONS 1 Basic...

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ME 365 EQUATIONS 1. Basic Statistics : Gaussian: 2 2 (x ) 2 1 p(x) e ; 2   E   g(X) g(x).p(x) dx ; i 1 X X ; N 22 x1 1 S (X X) ; N1 X X 0.5 ; N  2. Regression 2 i i i i Y f(X ) N ; J N ; 2 i i i i i i i i i o 1 o 1 i i Y X X X Y N X Y X Y ˆˆ f(x) a a x ; a ; a ; N (X ) ( X ) ;              TT ˆ y A a n ; A y A A a ; 2 1 2 i i 2 2 n n i i i XX 11 ˆ ˆ var( ) ; ; (Y f(X )) N2 XN        -1 a A A A A n i i yi ˆ adjusted R 1 ; unadjusted R 1 ˆ Y)     3. Confidence Intervals ˆ ,100Q Y ˆ Yt  4. Propagation of Error 2 2 2 2 2 x X,y Y ff Z f(X X , Y Y) f(X , Y) Z z x y xy            5. Digital Instrumentation nn nominal range true range Q; 2 2 1 a n 1 t; 2f s appear actual f K f f ;  Coding and decoding formulae, you need to know these. f s /2 f s 3f s /2 2f s Apparent frequency Q Code Voltage f s /2 Signal frequency

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6. First and Second Order Systems y y Kf(t)   2 n n 12 y y y Unit step response solutions (f(t)=1 for t>0): First order--   1 t y t K e     Second order--                 22 2 21 2 11 2 1 Underdamped 1 sin 1 tan 1 Critically damped 1 1 Overdamped 1 Zero damping 1 cos n n nn t n t n tt n e y t K t y t K e t ee y t K y t K     n t 7. Frequency Response Function and Filters K T(j ) 1j     ; Kj     ; 2 K [1 ( / ) ] 2j ( / )       ; no    8. System Identification: T = T(j ) denotes the Frequency Response Function final initial final yy 1 ln t y y(t)    i in 1 1 ln ,
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equationsheetfull_SP10 - ME 365 EQUATIONS 1 Basic...

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