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EE 302 HW1-2010

# EE 302 HW1-2010 - EE 302 Introduction to Feedback Systems...

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EE 302 Introduction to Feedback Systems HW 1, Spring 2010 Problem 1 a) Shown in the figure is a fluid- coupled mechanical rotational system. Torque is applied to the outer cylinder having inertia J 1 . Energy is coupled to inertia J 2 through the fluid viscosity B 1 . Write the differential equations for this system. b) Use the equations of (a) to find the transfer function θ 2 (s)/T(s), where T(s) = L[T(t)]. Problem 2 Figure P 2 a) Write the differential equations for the mechanical system shown in the figure. There are no applied forces; the system is excited only by initial conditions. b) A forc e f(t) is applied downward to the mass M, as shown in Figure (b). Find the transfer function from the applied force to the displacement, x 1 (t), of the mass; that is, find X 1 (s)/F(s). c) Repeat (a) and (b) for the system of Figure (c). J 2 J 1 Fluid, B 1 B 2 τ , θ 1 θ 2 M B K 1 K 2 x 1 x 2 M B K 1 x 1 x 2 M B K 1 x 1 x 2 f(t) (a) (b) (c)

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Problem 3 Consider the mechanical systems shown in the figure. a)
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EE 302 HW1-2010 - EE 302 Introduction to Feedback Systems...

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