X Φ 0 1) (20 marks) Consider a beam and ball arrangement like that shown above. A bushed DC motor rotates the beam about

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X Φ 0 1) (20 marks) Consider a beam and ball arrangement like that shown above. A bushed DC motor rotates the beam about the origin "O". The orange ring rolls along the beam and does not slide. Three variables describe the position of the two objects. Ⓒ =0 when the beam is horizontal p = 0 when the ball is above the origin x = 0 when the ball is above the origin The ball has mass m, and radius r. The beam has inertia JB. The motor has inertia Jm. Derive an equation of motion that relates the voltage applied to the DC motor, V(t), and the linear position of the ring, x(t). Use the small angle approximation for 8, ignore inductance and motor friction, but do not assume small values of x.