This will be the first lecture. Number one, vibration. Introduction to Vibration. There are many vibration courses available even in massive online open course. Then why reintroduce vibration course here? The objective of this course are first because this lecture is related with introduction to acoustics course. I especially try to link the vibration concept to acoustic concept. So in whole this lecture, you will learn about how the vibration phenomena is related with acoustics. That's our first objective. The second objective is, usually vibration theory has to do with many complicated mathematical approach. But in this course, we try to minimize mathematical approach. Rather than using complicated mathematical expression, we will simplify the approach, try to introduce the basic concept of vibrations so that you can use the simple understanding to your practical problem. So first objective is how vibration is related with acoustics. That's what I'm going to explore throughout this course. Second objective. Use the simplest mathematical approach to understand basic concept of vibration. That's our objective. Then, let's start with to understand vibration. What is vibration? If you look at the famous well-known dictionary, the dictionary says vibration is oscillation of things from the equilibrium. The next question is what is oscillation? Oscillation with the respect to equilibrium. Let me introduce very simple oscillation to you that will be this kind of oscillation, or anything like this, or oscillation like this. As you can see, oscillation is something moving back and forth with respect to equilibrium. That's pretty much conceptual description. If you transform this concept or a description into graphical expression, that will be easier to understand the oscillation with respect to equilibrium. So I will draw simply the oscillation with respect to equilibrium graphically. Okay, that will look like this. Then, where do you see equilibrium? Equilibrium would be some where around this. So this is the oscillation of a something with respect to equilibrium. The next question, how we describe this oscillation with respect to equilibrium? Or how to measure this oscillation with respect to equilibrium. To measure something we need to invite measurement coordinate. So we need to invite coordinate, then measure this oscillation. Say this is x, and this oscillation is varying with respect to time. Then, this coordinate, we can express this as t, that is time. Let me demonstrate two different oscillation. One is like oscillation like this, or in acoustic call expression, oscillation sounds like this. You can hear the oscillation. If you measured this oscillation with respect to time, graphically that will look like. Okay, different oscillation. You can hear two different oscillation that has a different, what? Different something. Different period, different pitch. Therefore, pitch or period, or you could say frequency, has to be one measure describing oscillation. How fast oscillation occurs with respect to time. So, let me briefly summarize. We first introduce the objective of this lecture and we introduce the basic concept of vibration. Vibration is oscillation of something with respect to equilibrium. We try to transform this understanding into graphical expression that look like this and then we introduce concept of frequency that expresses, describes the oscillation of something with respect to time. So, what is the frequency? In other words, how often oscillation moving back and forth occurs with respect to time? Okay, let me draw the simple frequency graph on an oscillation with respect to time over here. Moving forward and backward. Or you could see other oscillation with different frequency like this. As you can see here, this oscillation occurs within this time, which we call period. So, frequency is related with a period. Period simply means the time required same oscillation occurs, right? In this sense, this oscillation occurs with respect to this period and that this period is half of this period. For frequency which is one kilohertz, I just introduce the major that describes the frequency, hertz. Hertz measure how often it oscillate with respect to unit time. So, one kilohertz, meaning that it oscillates thousand times with respect to one second. This is two kilohertz, if you like you can measure it. Meaning that it oscillate with respect to time or with respect to one unit time 2,000 times. So, if I combine this two oscillation, then this will give me oscillation with respect to time over here. This is T, one period. It may look like, I don't know whether I can describe very well, but it may look like over here, it has to be this amount over here. I don't know how to. Okay, over here, this is minus, this is plus and zero. So, this is zero, but this has to be. Over here, say this is for example, one-half, this is one, this is one-half, then over here, that will be one. Here's one, zero. Over here, that will be a little bit more than one-half, so like that. So, it may look like. Then over here, this will be one-half minus, there will be zero again. So, look like something more complicated than this, okay? So, this complicated wave oscillation form has two component which is together. So, from this example, we can say, general oscillation like this can be expressed this oscillation, this oscillation and [inaudible] , this oscillation. This essentially describes the Fourier expression of oscillation. Fourier expression of oscillation simply decompose any arbitrary oscillation into many periodic oscillation.