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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

[tex]\int (kx + mg)dy[/tex] from -y to y0 would give me [tex]- \frac{1}{2}ky^{2}+mgy[/tex] 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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# Hanging Mass on Spring

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