Hi, I looked around for hours but it seems like I'm the only one who finds it confusing. I understand the concept of potential energy and work, but have a problem with the equations. Here is what I don't understand: The work energy theorem states that K2-K1=W. W = ∫Fdx from evaluated between x2 and 1. The Force done by a spring is -kx, so when only the spring acts on the body the equation should be: K2-K1=-½kx22 + ½kx12 K2+½kx22=K1+½kx12 But now, since W=-U(x) (potential energy) the equation turns out to be: K2-½kx22=K1-½kx12 For the total energy balance (kinetic + potential). But the lectures and examples I saw, and also the logical thing as I understand it, is that the equation should be K2+½kx22=K1+½kx12 for the kinetic + potential energy balance. Why do I get the signs wrong? Here's an example for a question which made me really confused: http://oyc.yale.edu/physics/phys-200/lecture-5#ch3 (minute 40:30). In short, a mass is hanged from a spring attached the ceiling, so the mass has 2 forces acting on it: gravity and the spring. In order to find the kinetic energy - potential energy equation, we have ΔKinetic_Energy = the negative of the work (-∫Fdx) of the total forces. Now I know that gravity acts downwards, so the force is -mg, and the spring's force is always -kx, so the equation should look something like this: K2-K1 = -∫F(gravity)dx - ∫F(spring)dx evaluated between x2 and 1. The negative signs before integrals is because we want to find the potential energy which is the negative of the work done. K2-K1 = -∫-mgdx - ∫-kxdx = ∫mgdx + ∫kxdx K2-K1 = mgx2 +½kx22 - mgx1 +½kx12 K2-mgx2-½kx22 = K1-mgx1-½kx12 which is the total energy equation. In class, they had the potential energy signs all opposite like this: K2+mgx2+½kx22 = K1+mgx1+½kx12 which of course looks more sensible and logical. The problem is that I can't see where I got the maths wrong. I follow the rules of and get it all messed up time and time again. Please, help me out here, this is driving me nuts! Ben.