 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, 0.785 radians, that's actually equal to one-eighth of a cycle. Remember again, one cycle is two pi radians. So what does this mean is if I were 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. Now here's a couple of special phase shifts. For this particular curve, my phase shift is 1.57 radians, or one-quarter of a cycle. And on this particular curve, my phase shift is 3.4 radians, half a cycle. You probably recognized right away that my 3.4 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. And what about the sign of the phase shift? By that I mean I could have a positive phase shift, or I could have a negative phase shift. Well that's what 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 0 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.