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fb3_22 - PROBLEM 3.22 KNOWN m = A sin 500m Constraint 8:1...

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Unformatted text preview: PROBLEM 3.22 KNOWN: m) = A sin 500m Constraint 8 :1 i002 Available 0),. = 120011: rad/s (recall (a [rad/s] = 231'sz Available values of 0.5 S Q S 1.5 FIND: q required to meet the dynamic error constraint ASSUMPTIONS: second order system SOLUTION For 8 5 10.02 , we want 0.98 S M(m) S 1.02. From the information given, the frequency ratio is (M0,. = 0.417. Then solving for Q in the equation (3.19), 0.98 5 1/10 - {aim}? + (29mm)2 "‘ yields 8 s 0.72 Repeating at the other limit, 1.02 s 1/[(l - {co/con?)2 + (Mm/muff“ yields 5 S 0.63 'I'hus,eitheratramduoerhavh1g8=0.650r0.7willwork. ...
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