%3Cp%3E%3Cbr%3E%3C%2Fp%3E%3Cp%3EProblem%201%26nbsp%3B%3C%2Fp%3E%3Cp%3EThe%26nbsp
ID: 1845676 • Letter: #
Question
%3Cp%3E%3Cbr%3E%3C%2Fp%3E%3Cp%3EProblem%201%26nbsp%3B%3C%2Fp%3E%3Cp%3EThe%26nbsp%3Bfollowing%26nbsp%3Btransfer%26nbsp%3Bfunction%26nbsp%3Bof%26nbsp%3Ba%26nbsp%3Blinear%26nbsp%3Bfilter%26nbsp%3Bis%26nbsp%3Bgiven%3A%3C%2Fp%3E%3Cp%3EH(s)%26nbsp%3B%3D%26nbsp%3B(2%2FLC)%2F(s%5E2%26nbsp%3B%2B%26nbsp%3BR%2FL%26nbsp%3Bs%26nbsp%3B%2B%26nbsp%3B2%2FLC)%3C%2Fp%3E%3Cp%3ELet%26nbsp%3BL%3D%26nbsp%3B2%26nbsp%3BHenry%2C%26nbsp%3BC%3D%26nbsp%3B1micro%26nbsp%3BFarad%26nbsp%3Band%26nbsp%3BR%26nbsp%3Bbe%26nbsp%3Bvariable.%3C%2Fp%3E%3Cp%3E1.1%26nbsp%3BPlot%26nbsp%3Bthe%26nbsp%3Blocus%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bsystem%26nbsp%3Bpoles%26nbsp%3Bas%26nbsp%3BR%26nbsp%3Bis%26nbsp%3Bvaried%26nbsp%3Bfrom%26nbsp%3Bzero%26nbsp%3Bto%26nbsp%3Binfinity.%3C%2Fp%3E%3Cp%3E1.2%26nbsp%3BIt%26nbsp%3Bis%26nbsp%3Bdesired%26nbsp%3Bto%26nbsp%3Bspecify%26nbsp%3BR%3DR1%26nbsp%3Bsuch%26nbsp%3Bthat%26nbsp%3Bthe%26nbsp%3Btwo%26nbsp%3Bpoles%26nbsp%3B(p)%26nbsp%3Bare%26nbsp%3Bcomplex%26nbsp%3Band%26nbsp%3B%7C%26nbsp%3BIm(p)%2FRe%26nbsp%3B(p)%7C%3D2.%3C%2Fp%3E%3Cp%3EWhere%26nbsp%3BIm%26nbsp%3Band%26nbsp%3BRe%2Crespectively%2C%26nbsp%3Bmean%26nbsp%3Bimaginary%26nbsp%3Band%26nbsp%3Breal.Derive%26nbsp%3BR%26nbsp%3Bgraphically%26nbsp%3Band%26nbsp%3Banalytically.%3C%2Fp%3E%3Cp%3E1.3%26nbsp%3BFor%26nbsp%3Bfour%26nbsp%3Bvalues%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bresistance%3A%26nbsp%3BR%3D0%2C%26nbsp%3BR%3DR1%2C%26nbsp%3BR%3D2000%26nbsp%3BOhms%26nbsp%3Band%26nbsp%3BR%3D%26nbsp%3B1500%26nbsp%3BOhms%2C%26nbsp%3Buse%26nbsp%3Bmatlab%26nbsp%3Bto%26nbsp%3Bderive%3C%2Fp%3E%3Cp%3Ethe%26nbsp%3Bunit%26nbsp%3Bstep%26nbsp%3Bresponse%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bsystem.%3C%2Fp%3E%3Cp%3E1.4%26nbsp%3BSpecify%26nbsp%3Bthe%26nbsp%3Bpercentage%26nbsp%3Bof%26nbsp%3Bovershoot%26nbsp%3Bfor%26nbsp%3Bthe%26nbsp%3Bunder-damped%26nbsp%3Bresponses%26nbsp%3Band%26nbsp%3Bthe%26nbsp%3Bfinal%26nbsp%3Berror.%3C%2Fp%3E%3Cp%3E%3Cbr%3E%3C%2Fp%3E%3Cp%3EProblem%26nbsp%3B2%26nbsp%3B%3C%2Fp%3E%3Cp%3EThe%26nbsp%3Bmass%26nbsp%3Bof%26nbsp%3Ba%26nbsp%3Bcar%26nbsp%3Bis%26nbsp%3B2000%26nbsp%3BKg.%26nbsp%3BThe%26nbsp%3Blinear%26nbsp%3Bspring%26nbsp%3Bconstant%26nbsp%3Bis%26nbsp%3B100%E2%80%99000%26nbsp%3BNewton%2Fm%26nbsp%3BThe%26nbsp%3Bgravity%26nbsp%3Bconstant%26nbsp%3Bis%26nbsp%3B10%26nbsp%3B%3C%2Fp%3E%3Cp%3Em%2Fsec%5E2%26nbsp%3Band%26nbsp%3Bthe%26nbsp%3Blinear%26nbsp%3Bshock%26nbsp%3Babsorber%26nbsp%3Bconstant%26nbsp%3Bmay%26nbsp%3Bhave%26nbsp%3Bone%26nbsp%3Bof%26nbsp%3Bthree%26nbsp%3Bvalues%3A%26nbsp%3BB%3D%26nbsp%3B0%2C%26nbsp%3BB%3DB1%3D%26nbsp%3B20%E2%80%99000%26nbsp%3B%3C%2Fp%3E%3Cp%3ENewton%2F%26nbsp%3Bm%2Fsec%2C%26nbsp%3BB%3D%26nbsp%3B2%26nbsp%3BB1%26nbsp%3Band%26nbsp%3BB%3DB2%3D%26nbsp%3B2.5%26nbsp%3BB1.%26nbsp%3BLet%26nbsp%3Bthe%26nbsp%3Bspring%26nbsp%3Band%26nbsp%3Bthe%26nbsp%3Bshock%26nbsp%3Babsorber%26nbsp%3Bbe%26nbsp%3Bconnected%26nbsp%3Bto%26nbsp%3Bthe%26nbsp%3B%3C%2Fp%3E%3Cp%3Eground.%3C%2Fp%3E%3Cp%3E2.1%26nbsp%3BDerive%26nbsp%3Ba%26nbsp%3Bsecond%26nbsp%3Border%26nbsp%3Bdifferential%26nbsp%3Bequation%26nbsp%3Bfor%26nbsp%3Bthe%26nbsp%3Bvibrations%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bcar%26nbsp%3Bup%26nbsp%3Band%26nbsp%3Bdown.%3C%2Fp%3E%3Cp%3E2.2%26nbsp%3BDerive%26nbsp%3Bthe%26nbsp%3Bdistance%26nbsp%3Bthat%26nbsp%3Bthe%26nbsp%3Bspring%26nbsp%3Bcompresses%26nbsp%3Bto%26nbsp%3Baccommodate%26nbsp%3Bthe%26nbsp%3Bweight%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bvehicle%26nbsp%3Bas%26nbsp%3Ba%26nbsp%3B%3C%2Fp%3E%3Cp%3Eparticular%26nbsp%3Bsolution%26nbsp%3Bto%26nbsp%3Bthe%26nbsp%3Bdifferential%26nbsp%3Bequation.%3C%2Fp%3E%3Cp%3E2.3%26nbsp%3BSuppose%26nbsp%3Ba%26nbsp%3Bstep%26nbsp%3Bof%26nbsp%3Bforce%26nbsp%3Bequal%26nbsp%3Bto%26nbsp%3Bthe%26nbsp%3Bweight%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bcar%26nbsp%3Bis%26nbsp%3Bapplied%26nbsp%3Bto%26nbsp%3Bthe%26nbsp%3Bcar%26nbsp%3Bdownwards.%26nbsp%3BUse%26nbsp%3Bmatlab%26nbsp%3B%3C%2Fp%3E%3Cp%3Eto%26nbsp%3Bderive%26nbsp%3Bthe%26nbsp%3Bunit%26nbsp%3Bstep%26nbsp%3Bresponse%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bsystem%26nbsp%3Bfor%26nbsp%3Beach%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bgiven%26nbsp%3Bfour%26nbsp%3Bvalues%26nbsp%3Bof%26nbsp%3BB.%3C%2Fp%3E%3Cp%3E%3Cbr%3E%3C%2Fp%3E%3Cp%3EProblem%26nbsp%3B3%26nbsp%3B%3C%2Fp%3E%3Cp%3EThe%26nbsp%3Btransfer%26nbsp%3Bfunction%26nbsp%3Bof%26nbsp%3Ba%26nbsp%3Bplant%26nbsp%3BG%26nbsp%3Bis%26nbsp%3Bgiven%26nbsp%3Bby%26nbsp%3B(0.5)%2F(s%5E2%26nbsp%3B%E2%80%93%26nbsp%3B9).%26nbsp%3BThe%26nbsp%3Bfeedback%26nbsp%3BH(s)%26nbsp%3B-%26nbsp%3Bconsisting%26nbsp%3Bof%26nbsp%3Bnegative%26nbsp%3B%3C%2Fp%3E%3Cp%3Eposition%26nbsp%3Band%26nbsp%3Bvelocity%26nbsp%3Bfeedback%26nbsp%3Bis%26nbsp%3B(4%26nbsp%3Bs%26nbsp%3B%2B%26nbsp%3B38).%26nbsp%3BThe%26nbsp%3Bcontroller%26nbsp%3Bis%26nbsp%3Bproportional%26nbsp%3Bcontrol%26nbsp%3Bwith%26nbsp%3Ba%26nbsp%3Bvariable%26nbsp%3Bgain%26nbsp%3BK.%3C%2Fp%3E%3Cp%3E3%26nbsp%3B.1%26nbsp%3BDerive%26nbsp%3Bthe%26nbsp%3Bclosed%26nbsp%3Bloop%26nbsp%3Btransfer%26nbsp%3Bfunction%26nbsp%3BC%2FR.%26nbsp%3B%3C%2Fp%3E%3Cp%3E3.2%26nbsp%3BSpecify%26nbsp%3Bthe%26nbsp%3Bpoles%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bclosed%26nbsp%3Bloop%26nbsp%3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