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timeresponse5

# timeresponse5 - Θ-Θ =(4 Combining equations(3 and(4 the...

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Time Response Q UESTION 5 For the system shown in Figure 5.1, determine the transfer function ( 29 ( 29 2 s s Θ Τ and the system’s percent overshoot, settling time, and peak time, assuming the system is underdamped. J B K τ (t) θ 1 (t) θ 2 (t) Figure 5.1 Summing the torques applied to the inertia ( 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 velocity of ω 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 ( 29 2 1 2 1 Js s s Bs s s Θ = Τ + Θ - Θ (3) ( 29 ( 29 ( 29

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Unformatted text preview: - Θ-Θ = (4) Combining equations (3) and (4), the transfer function is ( 29 ( 29 2 2 1 s J K K s s s B J Θ = Τ + + (5) Time Response Assuming the system is underdamped, the damping ratio and natural frequency, respectively, are 2 KJ B ζ = and n K J ϖ = . The system’s percent overshoot, settling time, and peak time, respectively, are 2 2 2 1 1 4 % 100 100 KJ B KJ B OS e e π ζπ - - - - = = (6) 4 8 s n B T K ζϖ = = (7) 2 2 1 1 4 p n T K KJ J B = =--(8) 2...
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timeresponse5 - Θ-Θ =(4 Combining equations(3 and(4 the...

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