mass connected to the ground with a spring and damper in parallel
Classic model used for deriving the equations of a mass spring damper model

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)

Deriving the equations of motion for this model is usually done by examining the sum of forces on the mass:

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 the solution will have an oscillatory component.

See also

References

  1. "Solving mass spring damper systems in MATLAB" (PDF).
  2. "Fast Simulation of Mass-Spring Systems" (PDF).


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.