# Simulation and modeling - Old Questions

1.  Differentiate between dynamic physical models and static physical models with example.

10 marks | Asked in 2068

Physical model is the smaller or larger physical copy of an object being modeled. The physical model helps in visualization of the object taken into consideration in an effective way. It is also used to solve equations with the particular boundary conditions.

Static Physical Model

- Static physical model is the physical model which describes relationships that do not change with respect to time.
- Such models only depict the object’s characteristics at any instance of time, considering that the object’s property will not change over time.
- Eg : An architectural model of a house, scale model of a ship and so on.

Dynamic Physical Model

- Dynamic physical model is the physical model which describes the time varying relationships of the object properties.
- Such models describes the characteristics of the object that changes over time.
- It rely upon the analogy between the system being studied and some other system of a different nature, but have similarity on forces that directs the behavior of the both systems.
- Eg: A model of wind tunnel, a model of automobile suspension and so on.

To illustrate this type of physical model, consider the two systems shown in following figures i.e. Figure 1 and Figure 2.

Fig1: Mechanical System

Fig2: Electrical system

The Figure 1. represents a mass that is subject to an applied force F(t) varying with time, a spring whose force is proportional to its extension or contraction, and a shock absorber 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 following differential equation.

Where,

x is the distance moved, M is the mass, K is the stiffness of the spring & D is the damping factor of the shock absorber.

Figure 2. represents an electrical circuit with an inductance L, a resistance R, and a capacitance C, connected in series with a voltage source that varies in time according to the function E(t). If q is the charge on the capacitance, it can be shown that the behavior of the circuit is governed by the following differential equation:

Inspection of these two equations shows that they have exactly the same form and that the following equivalences occur between the quantities in the two systems:

a) Displacement x = Charge q
b) Velocity x’ = Current I, q’
c) Force F = Voltage E
d) Mass M = Inductance L
e) Damping Factor D = Resistance R
f) Spring stiffness K = Inverse of Capacitance 1/C
g) Acceleration x’’ = Rate of change of current q’’

The mechanical system and the electrical system are analogs of each other, and the performance of either can be studied with the other.