Mass-spring-damper model
![mass connected to the ground with a spring and damper in parallel](http://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Mass_spring_damper.svg/220px-Mass_spring_damper.svg.png)
The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity. Packages such as MATLAB may be used to run simulations of such models.[1] As well as engineering simulation, these systems have applications in computer graphics and computer animation.[2]
Derivation (Single Mass)
[edit]Deriving the equations of motion for this model is usually done by summing the forces on the mass (including any applied external forces :
By rearranging this equation, we can derive the standard form:
- where
is the undamped natural frequency and is the damping ratio. The homogeneous equation for the mass spring system is:
This has the solution:
If then is negative, meaning the square root will be negative and therefore the solution will have an oscillatory component.
See also
[edit]References
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