For example if i am standing on top of the empire state building and i define that to be height=0 and i define the downward direction to be positive. if i drop a mass does its potential energy increase based on my definition of direction?

My actual problem was an exam question we were asked to find the equation of motion of atwoods machine using energy conservation.

the way i defined it on the exam is the same way i described it previously. and instead of getting x(dbl dot) = g(m1-m2)/(m1+m2)

i came up with an extra minus sign in front of the g in the numerator....

is this wrong. should the equation of motion come out the same no matter how you define your directions ( as long as you are consistent)