The cart with an inverted pendulum, shown below, is "bumped" with an impulse f...

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The cart with an inverted pendulum, shown below, is "bumped" with an impulse force, F. Determine the dynamic equations of motion for the system, and lin earize about the pendulum s angle, theta = Pi (in other words, assume that p endulum does not move more than a few degrees away from the vertical, chosen to be at an angle of Pi). Find a controller to satisfy all of the design re quirements given below. -The cart with an inverted pendulum, shown below, is "bumped" with an impulse force, F. Determine the dynamic equations of motion for the system, and lin earize about the pendulum s angle, theta = Pi (in other words, assume that p endulum does not move more than a few degrees away from the vertical, chosen to be at an angle of Pi). Find a controller to satisfy all of the design re quirements given below.