 Now we look at the potential energy of a spring. Potential energy, again, is energy which has been stored. And more specifically, we're looking at situations here where there's a mechanical force ready to do work. Now, for the case of a spring, if that spring is stretched or compressed, then there's a restoring force, which is ready to move it back to the equilibrium position. So stretching or compressing a spring stores a little bit of energy in that spring. Now if I look at the relationship between potential energy and work, the potential energy stored is equal to the outside mechanical work needed to prepare the system. Now for a spring, that would be looking at what is the external work needed in order to stretch or compress the spring from equilibrium. And from our earlier studies, we show that that was 1 half kx squared. So that means that the potential energy is going to be that same 1 half kx squared. Now looking at this in a little bit more detail, the energy stored in the spring could be written as the potential energy of the spring is 1 half kx squared, where that k is our spring constant. And the x is the distance it's stretched or compressed from equilibrium. And that's true even if the spring is vertically oriented, so that it's actually a y distance. But we're still going to use our symbol x to show the distance from equilibrium. Now occasionally textbooks will use slightly different symbols like e spring instead of this p e sub s. I've also seen ones that use u for the potential energy. And so u s is a spring potential energy. Some textbooks just use u without specifying what type of potential energy it is. So look at a quick example here. If I've got a 500 Newton per meter spring, which is stretched 0.5 meters from equilibrium, what's my potential energy going to be? Well, starting with my equation here, I recognize that this 500 Newton per meter, that's my spring constant, so that's going to go in for k. And the 0.5 meters, that's my distance, so that's going to go in for x. So plugging those numbers in and remembering to square that x value, I'd end up with 62.5 joules. Now just to note here on the units real quick, if I've got a Newton per meter and I multiply it by a meter squared, one of those meters canceled and I'm left with Newton meters, which is equivalent to a joule. So there's your potential energy on a spring.