 Now we introduce the equation for simple harmonic motion and this is the general equation that can be used for several situations. The equation itself looks like this. X of t equals a cosine omega t plus phi. X is my position of the oscillator. And notice it's a function of t because t is my time variable. So at different times I'll be at different positions. A stands for the amplitude. Omega is the angular frequency and phi is the phase. Now for any particular problem these three down here on the bottom, the amplitude angular frequency and phase are generally a constant for a specific situation. But t will vary causing your position to vary. So let's look at some of these in a little more detail. Amplitude. Amplitude has the symbol of a capital A. And it's the maximum displacement of an oscillator as it's moving back and forth. It's measured from the equilibrium position. It can be measured in any of the standard distance units. So the standard unit would be meters but you could also use any of the other distance measurements like feet or inches or anything like that. Angular frequency. Well its symbol is this omega. And yes that's the Greek letter omega not just a W. But its name is not omega. Its name is the angular frequency. And it's really a measure of how fast the oscillator goes through the cycle. In terms of its units it must be in radians per second. And we need our angular frequency in radians per second in order for some other things in the equation to work out correctly. Then we get to phase. It has a symbol of the Greek letter phi. And sometimes it's called phase. Sometimes it's called phase shift. Sometimes it's called phase constant. You might see some different names represented for it there. And it's really a measure of where the oscillation started in the cycle. So your phi value is going to be somewhere between zero and two pi radians. And it could be equal to zero or anywhere up to two pi. But it must be in units of radians for this equation. So since we've been talking a little bit about the units let's look at the units overall for the whole equation. We're going to start with this section in here in parentheses. Starting with our angular frequency which has units of radians per second. Followed by our t, our time variable which has units of seconds. And for this part of the equation we see that the two seconds can cancel each other out leaving just radians. Then we've got phi and so we have radians plus radians. Well radians plus radians really just gives me radians. So if I take the cosine of a number which has units of radians your calculator must be in radian mode to do that cosine calculation. But once you've done the cosine calculation I don't have any units anymore. The radians was an internal unit to the cosine function. That means we have just the amplitude and the position left. So if I express my amplitude in meters that means my end result position is also going to be measured in meters. If I were to give the amplitude in centimeters my position would be in centimeters. Or even feet or any other unit in there. So that's our equation for simple harmonic motion, SHM.