Mass-spring-damper model: Difference between revisions
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== Derivation (Single Mass) == |
== Derivation (Single Mass) == |
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Deriving the equations of motion for this model is usually done by |
Deriving the equations of motion for this model is usually done by summing the forces on the mass (including any applied external forces <math>F_\text{external})</math>: |
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:<math>\Sigma F = -kx - c \dot x +F_{external} = m \ddot x </math> |
:<math>\Sigma F = -kx - c \dot x +F_\text{external} = m \ddot x </math> |
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By rearranging this equation, we can derive the standard form: |
By rearranging this equation, we can derive the standard form: |
Latest revision as of 08:07, 22 April 2024
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[edit]