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modeling15 - Modeling QUESTION 15 For the system shown in...

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Modeling Q UESTION 15 For the system shown in Figure 15, set up the equations in matrix form that would allow you to determine the transfer function ( 29 ( 29 L s s θ Τ . Assume the gears are massless. r 1 r 2 J 1 B K θ L (t) J L τ (t) r 4 r 3 B L Figure 15 The Free Body Diagrams are given in Figure 15.1 below and the gears with radii r 2 and r 3 rotate with angular positions θ 2 and θ 3 , respectively. Note that the schematic between the damper and the spring is free to rotate at a unique angular position, which is denoted θ . To analyze this portion, a rotational mass with inertia J 0 = 0 is inserted. For the gear set on the left the following relationship holds 1 1 2 2 2 1 r r τ θ τ θ = = where τ 1 and τ 2 are the torques acting on the gears with radii r 1 and r 2 , respectively. For the gear set on the right the following relationships hold 3 3 4 4 3 L r r τ θ τ θ = = where τ 3 and τ 4 are the torques acting on the gears with radii r 3 and r 4 , respectively. Summing the
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