Let me start with the little bit of review of what we learned in the last two lectures. We attempted to understand fundamentals of vibration by traveling actually in three regions. One is mathematical, what I call math domain, and then we often travel to the physical domain, and then, often, we travel to a practical domain or I could say practical application domain. Those three field are interconnected. For example, in the last lecture, we talked about the single degree of freedom system which was graphically depicted like this. I have a mass and a spring. The mathematical expression of, this is physical representation was mx doubled up plus kx equal to F of t, where F of t is the excitation force applied upon mass and the x is the coordinated measures, the rest pass of this single degree of freedom system. Now, we start with a very simple case in which the F of t is equal to zero. In other words, there is no excitation force but allowing initial condition, initial displacement. That brings us a very interesting output, it says, from this mathematical expression when we have only initial condition, we obtained very interesting result that says natural frequency is equal to k over m. Therefore, it's saying that the regard, the relation with natural frequency scare with systems characteristics of that is spring constant and the mass m. A practical application by using this interesting result will be exciting the system with the initial displacement or initial velocity, we can obtain natural frequency of the system. If I know the stiffness or mass of the system, for example, for automobile up and down motion case, we do know the mass of the automobile, in major the natural frequency and we can estimate the stiffness in this direction. Suspension systems stiffness and this motion we can get the suspension systems stiffness. Then next moves on, what if we have a general f of t, general force f of t? There are many different kind of general forces. Then the next question is how to mathematically express general forces.