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Unformatted text preview: 3- 54Problems and Solutions Section 3.5 (3.39 through 3.42) 3.39Calculate the mean-square response of a system to an input force of constant PSD, S, and frequency response function H!( )=103+2j!( )Solution: Given: Sff=Sand H!( )=103+2j!The mean square of the response can be found from Eqs (3.66) and (3.68): x2=E x2!&quot;#$=%&amp;&amp;H(( )2Sff(( )d(x2=S%&amp;&amp;103+2j(2d(Using Eq. (3.67) yields x2=50!S33- 553.40Consider the base excitation problem of Section 2.4 as applied to an automobile model of Example 2.4.1 and illustrated in Figure 2.16. In this problem let the road have a random stationary cross section producing a PSD of S. Calculate the PSD of the response and the mean-square value of the response. Solution: Given: Sff=SFrom example 2.4.1: m=1007 kg, c=2000 kg/s, k=40,000 N/m!=c2km=20002 40000i1007=0.157 (underdamped)So, H!( )=1k&quot;m!2+jc!=14#104&quot;1007!2+2000j!H!( )2=14#104&quot;1007!2( )2+2000( )2j!...
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This note was uploaded on 03/31/2009 for the course MECHANICAL MAE351 taught by Professor J.g.lee during the Spring '09 term at Korea Advanced Institute of Science and Technology.
- Spring '09