A pendulum is attached to a motor shaft as in the figure. The motor is placed...

 

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A pendulum is attached to a motor shaft as in the figure. The motor is placed on a cart, and its position is x. The angular position of the pendulum is denoted with a. The lateral surface is frictionless but motor shaft has a viscous friction with a coefficient B. Motor inertia is omittable compared to pendulum. The rest of the parameters are on the figure. a) Assume that the motor is open circuit and derive governing equations (equation of motion) using Euler Lagrange method. b) Assume that the motor is open circuit and pendulum has an initial angle α₁ and released. Draw the angular position a and linear position x with respect to time. (No external forces). Pay attention to the equation of motion. The answer lies in the solution of the differential equation. c) Assume that the motor is closed circuit, Note that the Mc Jm Tm Km M K₂ V1 Mp g 60 equation of motion changes. How many generalized coordinates you have? What are they? d) Assume that the motor is closed circuit and pendulum has an initial angle a₁and released. Draw the angular position a and linear position x with respect to time. (No external forces). How does closed circuit motor effect the motion? A pendulum is attached to a motor shaft as in the figure. The motor is placed on a cart, and its position is x. The angular position of the pendulum is denoted with a. The lateral surface is frictionless but motor shaft has a viscous friction with a coefficient B. Motor inertia is omittable compared to pendulum. The rest of the parameters are on the figure. a) Assume that the motor is open circuit and derive governing equations (equation of motion) using Euler Lagrange method. b) Assume that the motor is open circuit and pendulum has an initial angle α₁ and released. Draw the angular position a and linear position x with respect to time. (No external forces). Pay attention to the equation of motion. The answer lies in the solution of the differential equation. c) Assume that the motor is closed circuit, Note that the Mc Jm Tm Km M K₂ V1 Mp g 60 equation of motion changes. How many generalized coordinates you have? What are they? d) Assume that the motor is closed circuit and pendulum has an initial angle a₁and released. Draw the angular position a and linear position x with respect to time. (No external forces). How does closed circuit motor effect the motion?