The Algorithm

1. Start by making a free body diagram 
2. Look at the axis you picked and choose one of the directions (eg. the X direction)
3. List the component for any forces that has any portion pointing in that direction.
4. Determine if the component is positive or negative based on your choice of axis.
5. Set this equal to the mass of the system times the acceleration of the system in the chosen direction.
6. If required for the problem, express each component as the magnitude and direction of the force (eq F_x = Fcos(theta) )
7. Go back to step two and repeat for the other direction(s)

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