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

Dynamic physical model
Dynamic physical models are ones which change with time or which are function of time. In wind tunnel, small aircraft models (static models) are kept and air is blown over them with different velocities and pressure profiles are measured with the help of transducers embedded in the model. Here wind velocity changes with time and is an example of dynamic physical model.

This model rely upon an analogy between the system being studied and some other system of different nature, the analogy usually depending upon an underlying similarities in the forces governing the behavior of the systems.

Consider two systems as shown in fig. fig. (a): Suspended weight attached with spring and piston of mechanical system. Fig (a) represents a mass that is subjected to an applied force 𝐹(𝑡) varying with time, a spring whose force is proportional to its extension or contraction, and shock absorber (Damper) that exerts a damping force proportional to the velocity of the mass. It can be shown that the motion of the system is described by the differential equation

𝑀𝑥̈ + 𝐷𝑥̇ + 𝑘𝑥 = 𝑘𝐹(𝑡) ………………… (𝑖)

Where, 𝑥 is distance moved
𝑀 is the mass,
𝐾 is the stiffness of spring,
𝐷 is the damping factor of Damper

Fig (b) represents an electrical circuit with an inductance𝐿, resistance 𝑅 and capacitance 𝐶 connected in series with a voltage source that varies in time according to function𝐸(𝑡). If 𝑞 is the charge on capacitor it can be shown that the barrier of the circuit is governed by following differential equation.

𝐿𝑞̈ + 𝑅𝑞̇ + (1/c)𝑞 = (1/𝑐)𝐸(𝑡) …………………. (𝑖𝑖)

From the above two equations (𝑖) and(𝑖𝑖),

 Mechanical Electrical 𝑥 q v ( 𝑥̇ ) i ( 𝑞̇ ) F ( t ) E ( t ) M L D R K 1/c

Thus, same mathematical model, by using different constants can give the solution for both mechanical and electric circuit.

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