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exam02_review

# exam02_review - ME 375 Spring 2011 Topics Covered on Exam...

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ME 375 – Spring 2011 Topics Covered on Exam No. 2 Steady-state response to harmonic excitation Y s ( ) = G s ( ) U s ( ) = N 1 s ( ) N 2 s ( ) ... N m s ( ) D 1 s ( ) D 2 s ( ) ... D n s ( ) U s ( ) For u t ( ) = sin ω t : y ss t ( ) = G j ω ( ) sin ω t + G j ω ( ) ( ) where 1 G j ω ( ) = Real 2 G j ω ( ) { } + Imag 2 G j ω ( ) { } = N 1 j ω ( ) N 2 j ω ( ) ... N m j ω ( ) D 1 j ω ( ) D 2 j ω ( ) ... D n j ω ( ) G j ω ( ) = tan 1 Imag G j ω ( ) { } Real G j ω ( ) { } = N 1 j ω ( ) + N 2 j ω ( ) + ... + N m j ω ( ) − ∠ D 1 j ω ( ) − ∠ D 2 j ω ( ) ... − ∠ D n j ω ( ) are the amplitude and phase frequency response functions (FRFs), respectively. Plots of G j ω ( ) dB and G j ω ( ) vs. ω (on a log 10 ω axis) are known as the Bode plots for the steady-state harmonic response. If N k s ( ) and D k s ( ) represent constant, linear and quadratic factors of the numerator and denominator of G s ( ) , respectively, the amplitude Bode plots for these factors can be approximated by the following dB lines/asymptotes 2 : K : constant 20 log 10 K ( ) straight line for all ω [EXACT] s ± 1 : straight-line for all ω with ± 20 dB / dec with

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exam02_review - ME 375 Spring 2011 Topics Covered on Exam...

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