For the mechanical translational system illustrated in Figure P3.1, write the differential equation relating the position...

  

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For the mechanical translational system illustrated in Figure P3.1, write the differential equation relating the position y(t) and the applied force f(t). eeeeeeee M₂0 eeeeeee (1) Vy (1) Figure P3.1 (b) Determine the transfer function Y(s)/F(s). (c) Determine the phase-variable canonical vector form of this system. 3.2. (a) For the mechanical translational system illustrated in Figure P3.2, write the differential equation relating the position y(t) and the applied force f(t). Figure P3.2 S(1) M₁ (b) Determine the transfer function Y(s)/F(s). B₁ 3 00000 K₁ M₂ 3 00000 K₂ M₂ (c) Determine the phase-variable canonical vector form of this system. By 3 L 00000 K₁ y (1) M₁ 3.3. (a) For the mechanical rotational system illustrated in Figure P3.3, write the differential equation relating T(t) and 8(t). Equilibrium position Figure P3.3 (b) Determine the transfer function (s)/T(s). K₁ ,do, (1) dt To = K' B3 √3 K₂ B₂ where K¹ is a constant, and that the inner gimbal's moment ... 1₂ K₁ B₁ 3.4. Figure P3.4 represents the diagram of a gyroscope which is used quite frequently in autopilots, stabilized fire control sys- tems, and so on. Assume that the rotor speed is constant, that the total developed torque about the output axis is given by am T(1) For the mechanical translational system illustrated in Figure P3.1, write the differential equation relating the position y(t) and the applied force f(t). eeeeeeee M₂0 eeeeeee (1) Vy (1) Figure P3.1 (b) Determine the transfer function Y(s)/F(s). (c) Determine the phase-variable canonical vector form of this system. 3.2. (a) For the mechanical translational system illustrated in Figure P3.2, write the differential equation relating the position y(t) and the applied force f(t). Figure P3.2 S(1) M₁ (b) Determine the transfer function Y(s)/F(s). B₁ 3 00000 K₁ M₂ 3 00000 K₂ M₂ (c) Determine the phase-variable canonical vector form of this system. By 3 L 00000 K₁ y (1) M₁ 3.3. (a) For the mechanical rotational system illustrated in Figure P3.3, write the differential equation relating T(t) and 8(t). Equilibrium position Figure P3.3 (b) Determine the transfer function (s)/T(s). K₁ ,do, (1) dt To = K' B3 √3 K₂ B₂ where K¹ is a constant, and that the inner gimbal's moment ... 1₂ K₁ B₁ 3.4. Figure P3.4 represents the diagram of a gyroscope which is used quite frequently in autopilots, stabilized fire control sys- tems, and so on. Assume that the rotor speed is constant, that the total developed torque about the output axis is given by am T(1)

Answer rating: 100% (QA)

To solve the differential equation in the image we can use the Laplace transform Taking the Laplace transform of both sides of the equation we get Ys ... View the full answer