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)
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:[3]
- where
is the undamped natural frequency and is the damping ratio.
See also[]
- Numerical methods
- Soft body dynamics#Spring/mass models
- Finite element analysis
References[]
- ^ "Solving mass spring damper systems in MATLAB" (PDF).
- ^ "Fast Simulation of Mass-Spring Systems" (PDF).
- ^ Longoria, Prof. R.G. "Modeling and Experimentation: Mass-Spring-Damper System Dynamics" (PDF). Retrieved 2019-11-19.
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Categories:
- Classical mechanics
- Mechanical vibrations
- Engineering stubs