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Mass-spring-damper model

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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)

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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 imaginary and therefore the solution will have an oscillatory component.[3]

See also

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References

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  1. ^ "Solving mass spring damper systems in MATLAB" (PDF).
  2. ^ "Fast Simulation of Mass-Spring Systems" (PDF).
  3. ^ "Introduction to Vibrations, Free Response Part 2: Spring-Mass Systems with Damping" (PDF). www.maplesoft.com. Retrieved 2024-09-22.