 Now we look at the conservation equation, and again, we're focusing on the conservation of mechanical energy for our physics one course. In these situations, conservation again means that the total mechanical energy stays the same. You could have transformations from one form of mechanical energy to another form of mechanical energy, but it stays as a type of mechanical energy. And you can have transfers of mechanical energy from one object to another within the system. Now again, our mechanical energy is the combination of kinetic plus potential. So the K e is the symbol I use for kinetic energy, and P e is the symbol I use for potential energy. And just as a reminder, some textbooks use different symbols for kinetic energy, maybe e sub k or just k by itself. And for potential energy, they might use e sub t, P, or a capital U. They don't use capital P because we're already using that for power, but a capital U is commonly used for potential energy as well. So our basic equation, again, we're saying that the total energy doesn't change. So that could be written out as delta e equals zero. Remember that delta means change of, so the change in energy is zero. We could also express this as the energy initial equals the energy final. And so whatever I have to start with for mechanical energy is the same as whatever I end up with for mechanical energy. So let's take that equation that my initial energy equals my final energy and just expand it out a little bit. Remember, the initial energy is a combination of kinetic and potential. And so is the final energy. So I have to look at the initial kinetic energy and the initial potential energy and the final kinetic energy and the final potential energy. In our course, we deal with two different forms of potential energy. So I can expand it out even further by looking at the potential energy of gravity and the potential energy of the spring. So I end up with three possible terms for my initial energy and three possible terms for my final mechanical energy. Now you may not have all three forms initially or finally in any particular problem, but you need to stop and think about do I have that form of energy and if you do include it in the equation. So when we have this equation, we can make a little bit more detailed one. So I'm going to take that fully expanded out one and just remind you that kinetic energy is one half mv squared. So I have to look at my initial velocity or my final velocity when I'm looking at my initial kinetic energy or my final kinetic energy. You have to consider your initial height or your final height to figure out whether or not you've got some potential energy of gravity. And finally, you have to look at your spring. Is there a spring and is it compressed or stretched initially? And is there a spring and is it compressed or stretched out finally? A lot of our problems that we're going to deal with will not have the spring potential energy. And it is actually possible that you could have a spring at the start and a different spring at the end. But most of the time is just a difference between how much it's stretched or compressed at the beginning and how much it's stretched or compressed at the end. So that's your conservation equation. We'll be using that when we solve various problems if we have a situation where there is conservation of mechanical energy.