## Idealization & FormulationEdit

In accord with how most engineers approach a problem, when we start studying systems we begin by taking a realistic problem and turning it into a specific mathematical formulation which will utilize known or currently developing techniques. It is standard to begin by taking a relatively complex and seemingly disordered system and creating a model which is simple, but also behaviorally correct. These simpler systems are called *idealized systems* and they are created by firstly having a deeply sophisticated understanding of the actual system and is derived from the actual system. When working in the derived idealized system, insight into the limitations of the actual system are developmentally realized; it is with this in mind that we always work from the ground up in all engineering and physical applications.
In the same way that in a first semester physics class you were trained to use a point-mass model when solving for a typical pulley/weight/etc. system and then move forward into more point-masses and eventually (as in a statics class) a distributed mass, we will move in the exact same ordering. Below you will see a few examples of increasingly complex idealistic modular representations:

Those are the classic steps towards approximating systems as done in a physics class. Next we will look at a schematic of a car and the models we will use throughout this text. These models are based off of the tire-suspension systems as well as the wheels and the body of the car. Below are the increasingly complex idealistic representations:

This text will nearly follow the above flow of modeling. There are also other vibration freedoms we will study; namely axial and torsional, and towards the very end nonlinear models.