 So now we're going to talk about period frequency and angular frequency. And this is in the context of oscillations. And for oscillations, it's any sort of repeating pattern of motion. For example, going around and around and around in a circle. Now we've been looking at a specific case of oscillations called simple harmonic motion. And we have a specific equation for that that we've been working with in physics. But instead of working with the equations, let's take a look at a simulation. And this is from the P-H-E-T site. And we've used that throughout the semester for a few things. So here's a simulation, masses and springs, that I've got preset up the way I want it to. And I've just got two different masses hanging out here on springs oscillating up and down. My repeating pattern of motion is the up and down cycle that it's going through. We'll come back to this a little bit later, but you'll notice these two have different motions between them. Now we get to the period. The period is the time for one oscillation cycle. And if I was thinking about this in terms of circular motion, which is where I first defined period, it's the time to go once around the circle. It's got a symbol of capital T. And make sure you're using capital T, not lowercase t. And the units for this is going to be seconds for our standard metric unit. But it could really be any time type unit, so you could use minutes or hours or whatever you need to use to express it. Flipping back over to my simulation here real quick, notice that these don't have the same period. The amount of time it takes mass number one to go up and down is a much longer, larger time than the shorter amount of time it takes spring number three and mass number three to go up and down. So this would have a short period, this would have a long period. Then we get into angular frequency. Angular frequency is also called angular speed if we're talking about circular motion, how fast it goes around that circle. And it's related to the period by the equation omega equals 2 pi over T, where omega is the angular frequency. T is my period that I talked about. If I think about the units for this, I'm going to have radians per second, where the second comes from the period, and the radian comes from the 2 pi because once around a cycle is 2 pi radians. Now we've got frequency, just regular frequency, one word. It's also related to the period by this equation, F equals 1 over T, where F is now my frequency, T is still my period. If I wanted to think about the units, this equation would imply that I've got 1 over seconds, and that's a perfectly fine unit to use for frequency. But a more general equation for my frequency might be the cycles per time. So if I go through multiple cycles, how many cycles do I go through and how much time? When I think about the equation that way, I could also represent the units as cycles per second. Now whether you think of it as 1 over seconds or cycles per second, there's a new unit called the Hertz HZ, which is used to represent frequency. Now these quantities are related to each other. So the angular frequency is related to the period, and the frequency is related to the period. And combining those, we can see that the angular frequency is related to the frequency, where my angular frequency is equal to 2 pi times my frequency. Now if I pop back over to my simulation really quick, notice that a short period has to do with a high frequency. It oscillates up and down more frequently than my slower one over here. So a long period, a large number for T, represents a low frequency or a small number for the frequency. So we can see two different periods and two different frequencies between these two oscillators. So that is our period and frequency introduction.