## Spring Mass Lesson 1
Model

The physical system is represented for the purposes of analysis by a physical model. Here is a sketch of the model with its key components, the spring and mass.

To keep the model simple, make the following assumptions:

- The spring obeys Hooke's law: the restoring force of the spring is directly proportional to the amount by which it is stretched or compressed.
- There is no damping: air resistance and friction are negligible.

Identify the relevant parameters:

- L: unstretched length of the spring
- m: mass attached to the spring
- k: spring constant (the constant of proportionality in Hooke's law), which characterizes the stiffness of the spring. A stiff spring has a large value of k.

Using the general methods of modeling

TUTORIAL: Basic Modeling Techniques

The mathematical model for the spring-mass system can be written as