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