 Now we can look at velocity and acceleration for simple harmonic motion. This quick review, I have my original equation for simple harmonic motion that was derived in one of the other videos, where x is the position and it's a function of t, the time variable. Now there's also some problem specific constants in here, the amplitude, angular frequency and phase. Also as a review from earlier this semester in physics, we know that the velocity is the derivative of the position with respect to time and the acceleration is the derivative of the velocity with respect to time. So that brings us to the velocity equation. I know it's going to be the derivative of the position x with respect to time and my x equation for simple harmonic motion is this one given here. So just combining those we see that the velocity is going to be the derivative with respect to time of this entire function here and time is the variable that I'm doing the derivative with respect to. Now you might have to go back and review your derivative rules because I've got a cosine and I've got a function of t inside that cosine. If I take care of those, what I end up getting is that the velocity as a function of time is going to be equal to minus a omega sine of omega t plus phi. Now I can take a look at the acceleration equation. My acceleration is the derivative of the velocity with respect to time and I just found that velocity in my last slide. So again I'm taking the derivative with respect to time of this function and this function includes a sine of a function with respect to time. So we're doing trig derivatives and the chain rule for derivatives. And once we've done that we come up with minus a omega squared cosine of omega t plus phi. So as a quick summary here is our equations for the position, velocity, and acceleration for our general equation for simple harmonic motion. If you are having troubles following those derivatives please feel free to ask your instructor.