timeresponse13

# timeresponse13 - Time Response QUESTION 13 For the system...

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Time Response Q UESTION 13 For the system shown in Figure 13, determine the transfer function ( 29 ( 29 2 s s Θ Τ . For J = 2 kg·m 2 , B = 2 N·m/(rad/s), and K = 2 N·m/rad, determine the system’s percent overshoot, settling time, and peak time. J B K τ (t) θ 1 (t) θ 2 (t) Figure 13 Summing the torques applied to the mass ( 29 ( 29 ( 29 ( 29 1 2 1 J t t B t t θ τ θ θ = + - && & & (1) The point between the damper and the spring is free to rotate with an angular displacement of θ 2 . Inserting a mass of zero at this point and summing the torques applied to this mass ( 29 ( 29 ( 29 2 1 2 0 B t t K t θ θ θ - - = & & (2) Taking the Laplace Transforms of equations (1) and (2), respectively, and assuming zero initial conditions ( 29 ( 29 ( 29 ( 29 2 1 2 1 Js s s Bs s s Θ = Τ + Θ - Θ (3) ( 29 ( 29 ( 29 ( 29 1 2 2 0 Bs s s K s θ θ θ

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