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;

𝑥̈+2𝜁𝑤𝑥̇+ 𝑤2𝑥= 𝑤2𝐹(𝑡)

Where, 2𝜁𝑤 = 𝐷/𝑀 and 𝑤2= 𝑘/𝑀

The solution can be given in terms of the variable𝑤(𝑡), where 𝑤 is the oscillation given by,

𝑤=2𝜋𝑓

And 𝑓 is the number of cycles per second The fig. shows how 𝑥 varies in response to a steady force applied at time𝑡=0. It can be seen that when 𝜁<1, the motion is oscillatory.

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