SolSec7.5 - Problems and Solutions Section 7.5(7.20-7.24...

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Unformatted text preview: Problems and Solutions Section 7.5 (7.20-7.24) 7.20 Using the definition of the mobility transfer function of Window 7.4, calculate the Re and Im parts of the frequency response function and hence verify equations (7.15) and (7.16). Solution: From Window 7.4: k cs ms s s F s sX + + = 2 29 ( 29 ( c j m k j ϖ ϖ ϖ ϖ α +- = 29 ( 29 ( 2 α ( w ) = jw ( k- mw 2 ) - jwc [ ] ( k- mw 2 ) 2 +( wc ) 2 2 2 2 2 2 ) ( ) ( ) ( ) ( c m k m k j c ϖ ϖ ϖ ϖ ϖ ϖ α +-- + = The previous expression can be separated into real and imaginary parts: Re α ( w ) [ ] = w 2 c ( k- w 2 m ) 2 + ( wc ) 2 Im [ ] 2 2 2 2 ) ( ) ( ) ( ) ( c m k m k w w w w w a +-- = 7.21 Using equations (7.15) and (7.16), verify that the Nyquist plot of the mobility frequency response function does in fact form a circle. Solution: Define A = ϖ 2 χ ( κ- ϖ 2 μ 29 2 + ( ϖχ 29 2- 1 2 χ = Ρε( α 29 - 1 2 χ B = ϖ ( κ- ϖ 2 μ 29 ( κ- ϖ 2 μ 29 2 + ( ϖχ 29 2 = Ιμ( α 29 Show that A 2 + Β 2 = 1 2 χ 2...
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SolSec7.5 - Problems and Solutions Section 7.5(7.20-7.24...

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