Understanding Potential Energy of Hanging Mass on Spring

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The discussion centers on understanding the potential energy of a mass attached to a hanging spring. The user is confused about the correct bounds for integration when calculating potential energy, considering the initial position of the spring as y0 = 0. They propose integrating from -y to y0, leading to a potential energy equation of -1/2 ky² + mgy. The user seeks clarification on whether this approach is valid or if they should use traditional bounds from y0 to y. Consistency in symbols and conventions is emphasized as crucial for accurate calculations.
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I'm having a little trouble understanding the concept of energy for a hanging spring. Suppose I have a system with a mass that is attached to a hanging spring and then is released, causing the mass to oscillate. I'm trying to determine the equation for potential energy, but I'm thrown off by signs.

I'm using the concept that potential is the negative integral of force.

I set my initial position of the spring to be be y0 = 0, so when the mass is attached, we're moving in the negative y direction. This leads me to believe that my bounds for integration should be from -y to y0.

\int (kx + mg)dy from -y to y0 would give me - \frac{1}{2}ky^{2}+mgy if I substitute in y0 = 0.

I guess my question is if I would be correct in integrating from -y to y0 in order to find potential as a function of position, or if I should integrate from y0 to y like I'm traditionally used to.
 
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it's never been a problem from which to which you'll integrate as long as you are consistent with the symbols and convention that you are using.
 
Ok that's what I thought thank you so much!
 

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