![Mass spring damper](https://upload.wikimedia.org/wikipedia/commons/4/45/Mass_spring_damper.svg)
The mass-spring-damper model consists of
discrete mass nodes distributed throughout an object and interconnected via a network of
spring
Spring(s) may refer to:
Common uses
* Spring (season), a season of the year
* Spring (device), a mechanical device that stores energy
* Spring (hydrology), a natural source of water
* Spring (mathematics), a geometric surface in the shape of a ...
s and
dampers. This model is well-suited for modelling object with complex material properties such as
nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
ity and
viscoelasticity
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...
.
Packages such as
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
may be used to run
simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...
s of such models. As well as engineering simulation, these systems have applications in
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
and
computer animation
Computer animation is the process used for digitally generating animations. The more general term computer-generated imagery (CGI) encompasses both static scenes (still images) and dynamic images (moving images), while computer animation refe ...
.
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
Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force.
The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all par ...
and
is the
damping ratio
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
.
See also
*
Numerical methods
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
*
Soft body dynamics#Spring/mass models
*
Finite element analysis
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
References
Classical mechanics
Mechanical vibrations
{{Engineering-stub