# Simulation and modeling - Old Questions

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

__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.