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Control ENG HW_Part_32 - Y(t = 1 je t 2 1 2(a jb(cos bt j...

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[ ] bt j bt jb a bt j bt jb a je t Y t sin )(cos ( ) sin )(cos ( 1 2 1 ) ( 2 - + - - + - - - - = - ξ τ τ ξ [ ] ) sin cos ( 2 1 2 1 ) ( 2 bt a bt b jb je t Y t + - - - = - ξ τ τ ξ [ ] ) sin( ) cos( 1 1 1 ) ( 2 2 t t e t Y t α ξ α ξ ξ τ ξ + - - - = - [ ] ξ ξ α 2 1 - = [ ] - = - ξ ξ φ 2 1 1 tan verified 8.14 From the figure in your text Y(4) for the system response is expressed b) verify that for , 1 = ξ and a step input τ τ t e t t Y - + - = 1 1 ) (
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1 1 1 ) ( 2 2 + + = s s s s Y τ τ 2 2 ) 1 ( ) 1 ( 1 ) ( + + + = + τ τ C Bs B A s s s Y 1 ) 1 2 ( 2 2 2 = + + + Cs Bs s s A τ τ 0 2 = + B A τ 0 2 = + C A τ A=1; 2 τ = B ; τ 2 = C ( ) 2 1 ) 1 ( 1 ) ( + +
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