Now we're ready to take a look at phase shift. As a reminder, here's our general equation for simple harmonic motion, abbreviated SHM. X again is the position, and it's a function of the time variable. There's three problem-specific constants in this problem, the amplitude, the angular frequency, and the phase. And phase is what we're taking a look at right now. So for phase shift, what is that? Well, it answers the question, where does the oscillation start in the cycle? And it's always going to be between zero and two pi radians. Now if the phase is equal to zero radians, that means that we're starting at our maximum displacement. That's where we say the standard cycle would start. Graphically, here's a cosine wave, and notice that at t equals zero, it's at its maximum position. So that means this one does have a phase shift of phi equals zero radians. Now I'm going to put another curve up there, which has a different phase shift. I'm still showing the old phi equals zero curve in red here, but now I've got my blue curve showing that at time equals zero, the position is not at a maximum. So that difference between where I'm at at time equals zero, and where I would have gotten to that point, is our phase shift. It's horizontal on the graph here. It's often measured up here at the top of the cycle, or down here at the bottom of the cycle, but it's actually the same little shift no matter where you are on it. Now for this particular phase shift, zero point seven eight five radians, that's actually equal to one eighth of a cycle. Remember again, one cycle is two pi radians. So what does this mean? I want to look at one cycle, say going from the minimum to the minimum. The phase shift is one eighth of that length. So I've shifted by one eighth of the total length of a cycle. Here's a couple of special phase shifts. For this particular curve, my phase shift is one point five seven radians, or one quarter of a cycle. And on this particular curve, my phase shift is three point four radians, half a cycle. You probably recognized right away that my three point four is pi. Since one cycle is two pi radians, half a cycle is pi radians. Which means this quarter of a cycle is actually pi over two. What about the sine of the phase shift? And by that, I mean I could have a positive phase shift, or I could have a negative phase shift. Well that's what two's two graphs would look like. Notice on the positive phase shift, my peak is always a little bit earlier than I would expect with a phi equals zero curve. And for a negative phase shift, my peak is always just a little bit late. So that shows me what my phase shift is really doing to the curve. So that's our basic introduction to phase shift for simple harmonic motion.