These graphs represent the force at the applied voltages. From this we can determine the amount of force the rod is subjected to. From there we can figure out , knowing all information about the inertias and characteristics of the rod, the amount of force required to return the rod to the center point when it falls in either direction. The rod will require a certain force when it reaches a certain angle and we can find that angle using the equation given to us from group 1.

 

 

 

 If we know the horizontal force, and all the characteristics of the rod, we can calculate the minimum amount of force required due to acceleration in the direction of the rods rotation. That minimum force would then act on the rod so as to change its direction of rotation, in effect causing it to return to a position of equilibrium. However, due to the imperfections of the motor and humanity, these results contain some degree of error. Resulting in either an overshoot or undershoot of the desired angular position. We prefer an overshoot, because if an undershoot occurs the rod will hit each side every time resulting in an automatic cutoff, eventually, of the motor, because the acceleration will not be great enough to effect the direction of the rods rotation.

  

Voltage Back acc.(ft/sec^2) forward acc (ft/sec^2) back force (N) forward force (N)
4 0.24469 0.108077 1.317 1.266
5 0.313939 0.158748 1.3425 1.285
8 0.97135 0.67543 1.5863 1.475
10 3.4088 2.11223 2.5 2.01
12 3.17 3.0 2.64 2.56

 

 

 

 

 

 I= moment of inertia of rod and weight = 2.048*10^-3 Kg*m^2