# Dynamic Mathematical Model | Types of System Model | Simulation and Modeling

## Dynamic mathematical model, a type of system model Simulation and Modeling Reference Notes BSc.CSIT Fifth Semester | Third year Tribhuvan University (TU)

Dynamic mathematical model
Dynamic mathematical model allows the changes of system attributes to be derived as a function of time. The derivation may be made with an analytical solution or with a numerical computation, depending upon the complexity of the model. The equation to describe the behavior of the car wheel is an example of a dynamic mathematical model. It is not possible to find analytic solution of this equation and one has to adopt the numerical methods. We divide equation by M and write in the following form;

π₯Μ+2ππ€π₯Μ+ π€2π₯= π€2πΉ(π‘)

Where, 2ππ€ = π·/π and π€2= π/π

The solution can be given in terms of the variableπ€(π‘), where π€ is the oscillation given by,

π€=2ππ

And π is the number of cycles per second

The fig. shows how π₯ varies in response to a steady force applied at timeπ‘=0. It can be seen that when π<1, the motion is oscillatory.

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