SolSec3_7 - 3 61Problems and Solutions for Section 3.7(3.45...

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Unformatted text preview: 3- 61Problems and Solutions for Section 3.7 (3.45 through 3.52) 3.45Using complex algebra, derive equation (3.89) from (3.86) with s= jω. Solution: From equation (3.86): H s( )=1ms2+cs+kSubstituting s=j!yields H j!( )=1m j!( )2+c j!( )+k=1k"m!2"cj!The magnitude is given by H j!dr( )=1m j!( )2+cj!( )+k"#$$%&’’=1k(m!2(cj!"#$%&’)*+++,-...1/2H j!( )=1k"m!2( )2+c!( )2which is Eq. (3.89) 3.46Using the plot in Figure 3.20, estimate the system’s parameters m, c, and k, as well as the natural frequency. Solution: From Fig. 3.20 1k=2!k=0.5"="n=0.25=km!m=81c"#4.6!c=0.0873- 623.47Using the values determined in Problem 3.46 plot the inertance transfer function's magnitude and phase for this system. Solution: From Problem 3.46 1k=2!k=0.5,"="n=0.25=km!m=8,1c"#4.6!c=0.087The inertance transfer function is given by Eq. (3.88): s2H s( )=s2ms2+cs+kSubstitute s=j!to get the frequency response function. The magnitude is given by: j!...
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SolSec3_7 - 3 61Problems and Solutions for Section 3.7(3.45...

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