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

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dynamic mathematical modelDynamic 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‘₯̈+2πœπ‘€π‘₯Μ‡+ 𝑀2π‘₯= 𝑀2𝐹(𝑑)

Where, 2πœπ‘€ = 𝐷/𝑀 and 𝑀2= π‘˜/𝑀

The solution can be given in terms of the variable𝑀(𝑑), where 𝑀 is the oscillation given by,

𝑀=2πœ‹π‘“

And 𝑓 is the number of cycles per second
displacement vs time

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

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