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. As well as engineering simulation, these systems have applications in computer graphics and computer animation.
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.