Simulation and Modelling - Old Questions
1. Differentiate between static and dynamic physical models in simulation. Describe dynamic physical model in detail with the help of suitable 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.
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.